1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# In the given figure, O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC = 7.5 cm, then the radius of the circle is _______

A
3.75 cm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
7.5 cm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
10.25 cm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
11.25 cm
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct option is D 11.25 cmAB = 15cm, AC = 7.5cm ∠AOB = 90°, since AB is a tangent to the circle. Let r be the radius of the circle. Therefore, OC = OB = r AO = AC + OC = 7.5 + r In △AOB, AO2 = AB2 + OB2 (7.5 + r)2 = 152 + r2 (15+2r2)2 = 225 + r2 225 + 4r2 + 60r = 900 + 4r2 60r = 900 - 225 r = 67560 = 11.25 cm. Therefore, option d is correct.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Chord Properties of Circles
MATHEMATICS
Watch in App
Join BYJU'S Learning Program