Question

In the given figure, PQR is a tangent to the circle at Q, whose centre is O and AB is a chord parallel to PR such that $\angle$ BQR = ${70}^o$, Then $\angle$ AQB = ?

(a) ${20}^o$ (b) ${35}^o$ (c) ${40}^o$ (d) ${45}^o$

Answer 1

Given: $PQR$ is a tangent to the circle $Q$

From the figure we can see

$AB||PR$
$\angle BQR={70}^0$
so$\angle BAQ=\angle BQR={70}^0$ ( alternate angles)
and $\angle ABQ=\angle BQR={70}^0$ ( as AB II PR)
By summing all the angles in triangle $ABQ$ , we get
$\angle BAQ+\angle ABQ+\angle AQB=180$
$\angle AQB=180°-70°-{70}^0$
Hence, $\angle AQB=40°$

correct option (c) 40°