A chord AB is drawn in a circle with center O. The tangent at A and the tangent at B meet at a point P. If ∠APB = 40°, measure the angle subtended by the chord AB at the circumference of the circle?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 70°.
∠APB = 40° between the two tangents from P.
∠APB + ∠AOB = 180° (since quadrilateral OAPB has two right angles)
So ∠AOB = 180° – 40° = 140°
Angle subtended by chord AB at the circumference = Half of ∠AOB = 140°/2 = 70°