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

# In the figure, BC is the diameter, PQ is the tangent, O is the centre of circle and ∠BAQ=65o. Find ∠AOC.

A
25o
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
65o
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
50o
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
30o
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C 50o We know tangent is always perpendicular to the radius at the point of contact. So, ∠OAQ=90o ∠OAB+∠BAQ=90o ∠OAB+65o=90o ∠OAB=90o−65o ∠OAB=25o In △OAB OA=OB (radius of circle) so, ∠OAB=∠OBA ∠OBA=25o Now, minor arc AC subtending ∠AOC at centre and ∠ABC at point B on the circumference of circle. So, ∠AOC=2∠ABC (angle made by arc at centre is double the angle made at any point on rest part of circumference of circle) ∠AOC=2×25o ∠AOC=50o So, option (c) correct.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Practice: Angle Subtended by an Arc at the Centre and on the Circle
MATHEMATICS
Watch in App
Join BYJU'S Learning Program