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
4.2k views
in Circles by (30.3k points)
closed by

In Fig. RQ is a tangent to the circle with centre O. If SQ = 6 cm and QR = 4 cm, then OR =

A. 8 cm 

B. 3 cm 

C. 2.5 cm 

D. 5 cm

1 Answer

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

Answer is D. 5 cm

Given: 

SQ = 6 cm 

QR = 4 cm 

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

By above property, ∆ROQ is right-angled at ∠OQR (i.e., ∠OQR = 90°). 

Diameter QS = 6 cm

Radius = \(\frac{Diameter }{2}\)

⇒Radius = \(\frac{6cm}{2}\)

⇒Radius (OQ) = 3 cm 

Now by Pythagoras theorem,

OR2 = OQ2 + QR2 

⇒ OR2 = 32 + 42 

⇒ OR2 = 9+ 16 

⇒ OR2 = 25 

⇒ OR= √25 

⇒ OR= 5 cm 

Hence, OR= 5 cm.

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

...