Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
1.2k views
in Circles by (30.3k points)
closed by

If TP and TQ are two tangents to a circle with centre O so that ∠POQ = 110°, then, ∠PTQ is equal to 

A. 60° 

B. 70° 

C. 80° 

D. 90°

1 Answer

+1 vote
by (30.5k points)
selected by
 
Best answer

Answer is B. 70°

Given: 

∠POQ = 110°

Property 1: The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency. 

Property 2: Sum of all angles of a quadrilateral = 360°.

By property 1, 

∠TPO = 90° 

∠TQO = 90° 

By property 2, 

∠POQ + ∠ TPO + ∠ TQO + ∠PTQ = 360° 

⇒ ∠PTQ = 360° - ∠POQ + ∠ TPO + ∠ TQO 

⇒ ∠PTQ = 360° - (110° + 90° + 90°) 

⇒ ∠PTQ = 360° - 290° 

⇒ ∠PTQ = 70° 

Hence, ∠PTQ = 70°

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...