Class 10 Exam > Class 10 Questions > two tangents tp and tq are drawn from an exte...
Start Learning for Free
two tangents tp and tq are drawn from an external point t to a circle they are inclined to each other at an angle of 100 degrees what is the measure of angle pqo?
Most Upvoted Answer
two tangents tp and tq are drawn from an external point t to a circle ...
Problem:
Two tangents TP and TQ are drawn from an external point T to a circle. They are inclined to each other at an angle of 100 degrees. What is the measure of angle PQO?
Solution:
Let O be the center of the circle.
Join OP and OQ.
Now, TP and TQ are tangents to the circle.
Therefore, OP and OQ are perpendicular to TP and TQ respectively.
So, angle PTO = 90 degrees and angle QTO = 90 degrees.
Also, angle TPO = angle TQO = 90 degrees (since TP and TQ are tangents).
Therefore, triangles TPO and TQO are right-angled triangles.
Thus, by trigonometry, we have:
tan (angle OPT) = TP/OP and tan (angle OQT) = TQ/OQ
Now, angle PTO = 90 degrees and angle QTO = 90 degrees.
Therefore, angle OPT + angle OQT = 180 - angle PQO (sum of angles in triangle OPQ).
Thus, we have:
tan (angle OPT) + tan (angle OQT) = TP/OP + TQ/OQ
Now, we are given that angle TPQ = 100 degrees.
Therefore, angle OPT + angle OQT = 180 - angle TPQ = 80 degrees.
Also, we know that OP = OQ (since O is the center of the circle).
Thus, we have:
tan (angle OPT) + tan (angle OQT) = 2TP/OP (since TQ = TP)
Putting the values of tan (angle OPT) + tan (angle OQT) and simplifying, we get:
tan (40 degrees) = TP/OP
Thus, angle PTO = 90 degrees and angle OPT = 40 degrees.
Therefore, angle OQP = angle OPT - angle TPQ = 40 - 100 = -60 degrees.
But angle OQP cannot be negative.
Therefore, we take angle OQP = 360 - 60 = 300 degrees.
Thus, angle PQO = angle PQT + angle TQO = 100 + 90 = 190 degrees.
Answer:
The measure of angle PQO is 190 degrees.
Community Answer
two tangents tp and tq are drawn from an external point t to a circle ...
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
two tangents tp and tq are drawn from an external point t to a circle they are inclined to each other at an angle of 100 degrees what is the measure of angle pqo? Related: Facts That Matter, Circles - Mathematics for Class 10th
Question Description
two tangents tp and tq are drawn from an external point t to a circle they are inclined to each other at an angle of 100 degrees what is the measure of angle pqo? Related: Facts That Matter, Circles - Mathematics for Class 10th for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about two tangents tp and tq are drawn from an external point t to a circle they are inclined to each other at an angle of 100 degrees what is the measure of angle pqo? Related: Facts That Matter, Circles - Mathematics for Class 10th covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for two tangents tp and tq are drawn from an external point t to a circle they are inclined to each other at an angle of 100 degrees what is the measure of angle pqo? Related: Facts That Matter, Circles - Mathematics for Class 10th.
two tangents tp and tq are drawn from an external point t to a circle they are inclined to each other at an angle of 100 degrees what is the measure of angle pqo? Related: Facts That Matter, Circles - Mathematics for Class 10th for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about two tangents tp and tq are drawn from an external point t to a circle they are inclined to each other at an angle of 100 degrees what is the measure of angle pqo? Related: Facts That Matter, Circles - Mathematics for Class 10th covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for two tangents tp and tq are drawn from an external point t to a circle they are inclined to each other at an angle of 100 degrees what is the measure of angle pqo? Related: Facts That Matter, Circles - Mathematics for Class 10th.
Solutions for two tangents tp and tq are drawn from an external point t to a circle they are inclined to each other at an angle of 100 degrees what is the measure of angle pqo? Related: Facts That Matter, Circles - Mathematics for Class 10th in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of two tangents tp and tq are drawn from an external point t to a circle they are inclined to each other at an angle of 100 degrees what is the measure of angle pqo? Related: Facts That Matter, Circles - Mathematics for Class 10th defined & explained in the simplest way possible. Besides giving the explanation of
two tangents tp and tq are drawn from an external point t to a circle they are inclined to each other at an angle of 100 degrees what is the measure of angle pqo? Related: Facts That Matter, Circles - Mathematics for Class 10th, a detailed solution for two tangents tp and tq are drawn from an external point t to a circle they are inclined to each other at an angle of 100 degrees what is the measure of angle pqo? Related: Facts That Matter, Circles - Mathematics for Class 10th has been provided alongside types of two tangents tp and tq are drawn from an external point t to a circle they are inclined to each other at an angle of 100 degrees what is the measure of angle pqo? Related: Facts That Matter, Circles - Mathematics for Class 10th theory, EduRev gives you an
ample number of questions to practice two tangents tp and tq are drawn from an external point t to a circle they are inclined to each other at an angle of 100 degrees what is the measure of angle pqo? Related: Facts That Matter, Circles - Mathematics for Class 10th tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup