Question

If AB is a chord of a circle, P and Q are the two points on the circle different from A and B, then
A. ∠APB=∠AQB
B. ∠APB+∠AQB = 180° or ∠APB=∠AQB
C. ∠APB+∠AQB=90°
D. ∠APB+∠AQB=180°

Answer 1

$\text{case(i) P and Q lie on different semicircles}$

$\text{Here, APBQ is a cyclic quadrilaterl}$

$\text{We know that}\;\textbf{"opposite angles of a cyclic quadrilateral are supplementary"}$

$\implies\angle{APB}+\angle{AQB}=180^{\circ}$

$\text{case(ii) P and Q lie on same semicircle}$

$\text{We know that}\;\textbf{"Angle in a semicircle is right angle"}$

$\implies\angle{APB}=\angle{AQB}=90^{\circ}$

$\text{In both the cases, we have}$

$\bf\;\angle{APB}+\angle{AQB}=180^{\circ}\;\text{or}\;\angle{APB}=\angle{AQB}$

$\therefore\textbf{Option B is correct}$