JEE Exam > JEE Questions > The triangle PQR is inscribed in the circle x...
Start Learning for Free
The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have coordinates (3, 4) and (–4, 3) respectively, then ∠QPR may be equal to
- a)π/2
- b)π/3
- c)π/4
- d)π/6
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R h...
(i.e. angle subtended at the centre of a circle is double the angle subtended in the alternate segment).Hence (c) is the correct answer.
Most Upvoted Answer
The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R h...
-3, -4), we can use these coordinates to find the coordinates of point P.
Since the triangle PQR is inscribed in the circle, the center of the circle is the midpoint of the line segment QR. We can find the midpoint using the average of the x-coordinates and the average of the y-coordinates.
Midpoint of QR = ((3 + (-3))/2, (4 + (-4))/2) = (0, 0)
Therefore, the center of the circle is (0, 0).
To find the coordinates of point P, we need to find the intersection of the circle with the line passing through points Q and R.
The equation of the line passing through Q and R can be found using the slope-intercept form:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
m = (y2 - y1) / (x2 - x1) = (4 - (-4)) / (3 - (-3)) = 8/6 = 4/3
Using point Q (3, 4), the equation of the line passing through Q and R is:
y - 4 = (4/3)(x - 3)
Simplifying the equation:
3y - 12 = 4x - 12
3y = 4x
y = (4/3)x
Substituting y into the equation of the circle:
x^2 + (4/3)x^2 = 25
(7/3)x^2 = 25
x^2 = (3/7)(25)
x^2 = 75/7
Taking the square root of both sides:
x = ± √(75/7)
Since the triangle PQR is inscribed in the circle, point P will have the same x-coordinate as either Q or R.
Therefore, the coordinates of point P are (± √(75/7), y), where y can be found by substituting x into the equation of the line:
y = (4/3)(± √(75/7)).
So the coordinates of point P are (± √(75/7), (4/3)(± √(75/7))).
Since the triangle PQR is inscribed in the circle, the center of the circle is the midpoint of the line segment QR. We can find the midpoint using the average of the x-coordinates and the average of the y-coordinates.
Midpoint of QR = ((3 + (-3))/2, (4 + (-4))/2) = (0, 0)
Therefore, the center of the circle is (0, 0).
To find the coordinates of point P, we need to find the intersection of the circle with the line passing through points Q and R.
The equation of the line passing through Q and R can be found using the slope-intercept form:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
m = (y2 - y1) / (x2 - x1) = (4 - (-4)) / (3 - (-3)) = 8/6 = 4/3
Using point Q (3, 4), the equation of the line passing through Q and R is:
y - 4 = (4/3)(x - 3)
Simplifying the equation:
3y - 12 = 4x - 12
3y = 4x
y = (4/3)x
Substituting y into the equation of the circle:
x^2 + (4/3)x^2 = 25
(7/3)x^2 = 25
x^2 = (3/7)(25)
x^2 = 75/7
Taking the square root of both sides:
x = ± √(75/7)
Since the triangle PQR is inscribed in the circle, point P will have the same x-coordinate as either Q or R.
Therefore, the coordinates of point P are (± √(75/7), y), where y can be found by substituting x into the equation of the line:
y = (4/3)(± √(75/7)).
So the coordinates of point P are (± √(75/7), (4/3)(± √(75/7))).
Community Answer
The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R h...
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have coordinates (3, 4) and (–4, 3) respectively, then ∠QPR may be equal toa)π/2b)π/3c)π/4d)π/6Correct answer is option 'C'. Can you explain this answer?
Question Description
The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have coordinates (3, 4) and (–4, 3) respectively, then ∠QPR may be equal toa)π/2b)π/3c)π/4d)π/6Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have coordinates (3, 4) and (–4, 3) respectively, then ∠QPR may be equal toa)π/2b)π/3c)π/4d)π/6Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have coordinates (3, 4) and (–4, 3) respectively, then ∠QPR may be equal toa)π/2b)π/3c)π/4d)π/6Correct answer is option 'C'. Can you explain this answer?.
The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have coordinates (3, 4) and (–4, 3) respectively, then ∠QPR may be equal toa)π/2b)π/3c)π/4d)π/6Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have coordinates (3, 4) and (–4, 3) respectively, then ∠QPR may be equal toa)π/2b)π/3c)π/4d)π/6Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have coordinates (3, 4) and (–4, 3) respectively, then ∠QPR may be equal toa)π/2b)π/3c)π/4d)π/6Correct answer is option 'C'. Can you explain this answer?.
Solutions for The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have coordinates (3, 4) and (–4, 3) respectively, then ∠QPR may be equal toa)π/2b)π/3c)π/4d)π/6Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have coordinates (3, 4) and (–4, 3) respectively, then ∠QPR may be equal toa)π/2b)π/3c)π/4d)π/6Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have coordinates (3, 4) and (–4, 3) respectively, then ∠QPR may be equal toa)π/2b)π/3c)π/4d)π/6Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have coordinates (3, 4) and (–4, 3) respectively, then ∠QPR may be equal toa)π/2b)π/3c)π/4d)π/6Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have coordinates (3, 4) and (–4, 3) respectively, then ∠QPR may be equal toa)π/2b)π/3c)π/4d)π/6Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have coordinates (3, 4) and (–4, 3) respectively, then ∠QPR may be equal toa)π/2b)π/3c)π/4d)π/6Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup