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Your email address will not be published. Save my name, email, and website in this browser for the next time I comment. Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information. The circumcenter is the point of junction of the three perpendicular bisectors.
The perpendicular bisector of a triangle is the lines drawn perpendicularly from the midpoint of the triangle. The term centroid is defined as the centre point of the object. The point at which the three medians of the triangle intersect or touch each other is recognised as the centroid of a triangle.
The orthocenter is the location where the three altitudes of a triangle meet. A line segment developed from one vertex to the opposite side, which is perpendicular to the opposite side, is known as the altitude of a triangle. the angle made at the circumference at the circle. Question 2: Three sides of a triangle are 40 cm, 58 cm and 42 cm. Find the distance between the orthocentre and the circumcenter of a triangle. Question 3: If the circumcenter of a triangle lies on one of the sides then the orthocenter of the triangle lies on?
Given that the circum-center lies on one of the sides of a triangle. Hence the triangle is a right angled triangle. In a right angled triangle the orthocenter is the vertex where the angle is 90°.
Therefore option 1 would be the answer. In the previous headings, we saw how to find the circumcenter of the triangle and the formula of circumcentre now let us learn some of the important properties of the circumcenter of a triangle. Check out this article on Number Systems.
The location for the circumcenter of a triangle is different for distinct types of triangles as follows. We hope that the above article on Circumcenter of a Triangle is helpful for your understanding and exam preparations.
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Supported with funding from the Arjay and Frances F. Miller Foundation and the James Irvine Foundation. California voters have now received their mail ballots, and the November 8 general election has entered its final stage.
Amid rising prices and economic uncertainty—as well as deep partisan divisions over social and political issues—Californians are processing a great deal of information to help them choose state constitutional officers and state legislators and to make policy decisions about state propositions.
The midterm election also features a closely divided Congress, with the likelihood that a few races in California may determine which party controls the US House. These are among the key findings of a statewide survey on state and national issues conducted from October 14 to 23 by the Public Policy Institute of California:.
Today, there is a wide partisan divide: seven in ten Democrats are optimistic about the direction of the state, while 91 percent of Republicans and 59 percent of independents are pessimistic.
Californians are much more pessimistic about the direction of the country than they are about the direction of the state. Majorities across all demographic groups and partisan groups, as well as across regions, are pessimistic about the direction of the United States. A wide partisan divide exists: most Democrats and independents say their financial situation is about the same as a year ago, while solid majorities of Republicans say they are worse off.
Regionally, about half in the San Francisco Bay Area and Los Angeles say they are about the same, while half in the Central Valley say they are worse off; residents elsewhere are divided between being worse off and the same.
The shares saying they are worse off decline as educational attainment increases. Strong majorities across partisan groups feel negatively, but Republicans and independents are much more likely than Democrats to say the economy is in poor shape.
Today, majorities across partisan, demographic, and regional groups say they are following news about the gubernatorial election either very or fairly closely. In the upcoming November 8 election, there will be seven state propositions for voters.
Due to time constraints, our survey only asked about three ballot measures: Propositions 26, 27, and For each, we read the proposition number, ballot, and ballot label. Two of the state ballot measures were also included in the September survey Propositions 27 and 30 , while Proposition 26 was not. This measure would allow in-person sports betting at racetracks and tribal casinos, requiring that racetracks and casinos offering sports betting make certain payments to the state to support state regulatory costs.
It also allows roulette and dice games at tribal casinos and adds a new way to enforce certain state gambling laws. Fewer than half of likely voters say the outcome of each of these state propositions is very important to them.
Today, 21 percent of likely voters say the outcome of Prop 26 is very important, 31 percent say the outcome of Prop 27 is very important, and 42 percent say the outcome of Prop 30 is very important. Today, when it comes to the importance of the outcome of Prop 26, one in four or fewer across partisan groups say it is very important to them.
About one in three across partisan groups say the outcome of Prop 27 is very important to them. Fewer than half across partisan groups say the outcome of Prop 30 is very important to them. When asked how they would vote if the election for the US House of Representatives were held today, 56 percent of likely voters say they would vote for or lean toward the Democratic candidate, while 39 percent would vote for or lean toward the Republican candidate.
Democratic candidates are preferred by a point margin in Democratic-held districts, while Republican candidates are preferred by a point margin in Republican-held districts. Abortion is another prominent issue in this election. When asked about the importance of abortion rights, 61 percent of likely voters say the issue is very important in determining their vote for Congress and another 20 percent say it is somewhat important; just 17 percent say it is not too or not at all important.
With the controlling party in Congress hanging in the balance, 51 percent of likely voters say they are extremely or very enthusiastic about voting for Congress this year; another 29 percent are somewhat enthusiastic while 19 percent are either not too or not at all enthusiastic.
Today, Democrats and Republicans have about equal levels of enthusiasm, while independents are much less likely to be extremely or very enthusiastic. As Californians prepare to vote in the upcoming midterm election, fewer than half of adults and likely voters are satisfied with the way democracy is working in the United States—and few are very satisfied.
Satisfaction was higher in our February survey when 53 percent of adults and 48 percent of likely voters were satisfied with democracy in America.
Today, half of Democrats and about four in ten independents are satisfied, compared to about one in five Republicans. Notably, four in ten Republicans are not at all satisfied. In addition to the lack of satisfaction with the way democracy is working, Californians are divided about whether Americans of different political positions can still come together and work out their differences. Forty-nine percent are optimistic, while 46 percent are pessimistic.
Today, in a rare moment of bipartisan agreement, about four in ten Democrats, Republicans, and independents are optimistic that Americans of different political views will be able to come together. Notably, in , half or more across parties, regions, and demographic groups were optimistic.
Today, about eight in ten Democrats—compared to about half of independents and about one in ten Republicans—approve of Governor Newsom. Across demographic groups, about half or more approve of how Governor Newsom is handling his job. Approval of Congress among adults has been below 40 percent for all of after seeing a brief run above 40 percent for all of Democrats are far more likely than Republicans to approve of Congress. Fewer than half across regions and demographic groups approve of Congress.
Approval in March was at 44 percent for adults and 39 percent for likely voters. Across demographic groups, about half or more approve among women, younger adults, African Americans, Asian Americans, and Latinos.
Views are similar across education and income groups, with just fewer than half approving. Approval in March was at 41 percent for adults and 36 percent for likely voters. Across regions, approval reaches a majority only in the San Francisco Bay Area. Across demographic groups, approval reaches a majority only among African Americans. This map highlights the five geographic regions for which we present results; these regions account for approximately 90 percent of the state population.
Residents of other geographic areas in gray are included in the results reported for all adults, registered voters, and likely voters, but sample sizes for these less-populous areas are not large enough to report separately.
The PPIC Statewide Survey is directed by Mark Baldassare, president and CEO and survey director at the Public Policy Institute of California.
Coauthors of this report include survey analyst Deja Thomas, who was the project manager for this survey; associate survey director and research fellow Dean Bonner; and survey analyst Rachel Lawler. The Californians and Their Government survey is supported with funding from the Arjay and Frances F. Findings in this report are based on a survey of 1, California adult residents, including 1, interviewed on cell phones and interviewed on landline telephones.
The sample included respondents reached by calling back respondents who had previously completed an interview in PPIC Statewide Surveys in the last six months. Interviews took an average of 19 minutes to complete. Interviewing took place on weekend days and weekday nights from October 14—23, Cell phone interviews were conducted using a computer-generated random sample of cell phone numbers. Additionally, we utilized a registration-based sample RBS of cell phone numbers for adults who are registered to vote in California.
All cell phone numbers with California area codes were eligible for selection. After a cell phone user was reached, the interviewer verified that this person was age 18 or older, a resident of California, and in a safe place to continue the survey e. Cell phone respondents were offered a small reimbursement to help defray the cost of the call.
Cell phone interviews were conducted with adults who have cell phone service only and with those who have both cell phone and landline service in the household. Landline interviews were conducted using a computer-generated random sample of telephone numbers that ensured that both listed and unlisted numbers were called. Additionally, we utilized a registration-based sample RBS of landline phone numbers for adults who are registered to vote in California.
All landline telephone exchanges in California were eligible for selection. For both cell phones and landlines, telephone numbers were called as many as eight times. When no contact with an individual was made, calls to a number were limited to six.
Also, to increase our ability to interview Asian American adults, we made up to three additional calls to phone numbers estimated by Survey Sampling International as likely to be associated with Asian American individuals. Accent on Languages, Inc. The survey sample was closely comparable to the ACS figures. To estimate landline and cell phone service in California, Abt Associates used state-level estimates released by the National Center for Health Statistics—which used data from the National Health Interview Survey NHIS and the ACS.
The estimates for California were then compared against landline and cell phone service reported in this survey. We also used voter registration data from the California Secretary of State to compare the party registration of registered voters in our sample to party registration statewide. The sampling error, taking design effects from weighting into consideration, is ±3. This means that 95 times out of , the results will be within 3. The sampling error for unweighted subgroups is larger: for the 1, registered voters, the sampling error is ±4.
For the sampling errors of additional subgroups, please see the table at the end of this section. Sampling error is only one type of error to which surveys are subject. Results may also be affected by factors such as question wording, question order, and survey timing.
We present results for five geographic regions, accounting for approximately 90 percent of the state population. Residents of other geographic areas are included in the results reported for all adults, registered voters, and likely voters, but sample sizes for these less-populous areas are not large enough to report separately.
We also present results for congressional districts currently held by Democrats or Republicans, based on residential zip code and party of the local US House member. We compare the opinions of those who report they are registered Democrats, registered Republicans, and no party preference or decline-to-state or independent voters; the results for those who say they are registered to vote in other parties are not large enough for separate analysis.
We also analyze the responses of likely voters—so designated per their responses to survey questions about voter registration, previous election participation, intentions to vote this year, attention to election news, and current interest in politics. The percentages presented in the report tables and in the questionnaire may not add to due to rounding. Additional details about our methodology can be found at www.
pdf and are available upon request through surveys ppic. October 14—23, 1, California adult residents; 1, California likely voters English, Spanish. Margin of error ±3.
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