In a circle with centre O, an arc ABC subtends an angle of 138^ at the centre. The chord AB is produced to a point P. Then the me…

Question

In a circle with centre O, an arc ABC subtends an angle of 138^ at the centre. The chord AB is produced to a point P. Then the measure of CBP is:

1. A. 42^
2. B. 111^
3. C. 69^ (Correct answer)
4. D. 108^

Correct Answer

Option C — 69^

Detailed Solution & Explanation

The correct answer is $69^\circ$.

Key Points

• Angle at the centre $=138^\circ$, so the inscribed angle $\angle ABC=\dfrac{138^\circ}{2}=69^\circ$ on the remaining arc.
• Since AB is produced to P, $\angle CBP$ is the exterior angle of the cyclic figure and equals the inscribed angle $=69^\circ$.