Geometry Practice Test 4

Question : 8 of 40

Marks: +1, -0

In the figure given above, ∠AOB = 46°; AC and OB intersect each other at right angles. What is the measure of ∠OBC? (O is the centre of the circle.)

Solution:

∠AOB = 46°
∠APO = ∠BPC = 90°
An angle subtended by an arc at the center is double that of the angle subtended by it at any point on the circle.

1/2

∠AOB = ∠ACB
∠ACB =

1/2 × 46°

= 23°

In ΔPCB,
∠PCB + ∠CPB + ∠PBC = 180°
23° + 90° + ∠PBC = 180°
∠PBC = 180°-113°
∠PBC = 67°
or ∠OBC = 67°

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