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

# AB is the longest chord of a circle with centre O. P is any point on the circumference of the circle, not coinciding with A or B. Find ∠APB in degrees.

A

75 degrees

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

80 degrees

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

100 degrees

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

90 degrees

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct option is D 90 degrees Consider the circle as shown, with centre O and AB as the longest chord. Since diameter is the longest chord, AB is the diameter. Recall that the angle subtended by an arc at the centre of the circle is twice the angle subtended by this arc in the other segment. Now the angle subtended by the arc at the centre is ∠AOB, which is 180∘. Let P be any point on the remaining part of the circle. Different positions of P are shown. In each case, ∠APB is the angle subtended by the arc in the other segment. So it should be half the angle subtended by the arc at the centre (which is 180∘). Half of 180∘ is 90∘. So ∠APB=90∘.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Drawing Tangents to a Circle
MATHEMATICS
Watch in App
Join BYJU'S Learning Program