A, B and C are points on a circle with centre O. The arc ABC (the arc from A to C that passes through B) subtends an angle of \(142^\circ\) at the centre. The chord AB is produced to a point P. What is the measure of \(\angle CBP\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 71°
The angle subtended by an arc at the centre is twice the angle it subtends at any point on the rest of the circle. \(\angle ABC\) stands on the arc AC that does not contain B.
Arc AC not containing B subtends \(360^\circ-142^\circ=218^\circ\) at the centre
\(\angle ABC=\frac{1}{2}\times218^\circ=109^\circ\)
A, B, P lie on one line, so \(\angle CBP=180^\circ-109^\circ=71^\circ\)
