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
24.5k views
in Circles by (47.3k points)
closed by

Two tangents PQ and PR are drawn from an external point to a circle with centre O. Prove that QORP is a cyclic quadrilateral.

1 Answer

+1 vote
by (48.7k points)
selected by
 
Best answer

We know that,

Radius ⊥ Tangent = OR ⊥ PR

i.e., ∠ORP = 90°

Likewise,

Radius ⊥ Tangent = OQ ⊥PQ

∠OQP = 90°

In quadrilateral ORPQ,

Sum of all interior angles = 360º

∠ORP + ∠RPQ+ ∠PQO + ∠QOR = 360º

90º + ∠RPQ + 90º + ∠QOR = 360º

Hence, ∠O + ∠P = 180o

PROQ is a cyclic quadrilateral.

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

...