MathematicsIn the given figure, O is the centre of the circle with chords AP and BP being produced to R and Q, respectively. If ∠QPR=350, then find the measure of ∠AOB.

In the given figure, $O$ is the centre of the circle with chords $AP$ and $BP$ being produced to $R$ and $Q$ , respectively. If $∠ QPR = 35^{0}$ , then find the measure of $∠ AOB$ .

A
$80^{o}$
B
$60^{o}$
C
$70^{o}$
D
$40^{o}$

Solution:

It is given that

∠ QPR = 35^{0}

and

O

is the centre of the circle with chords

AP

and

BP

being produced to

R

and

Q

, respectively.
We need to find the measure of

∠ AOB .

Consider the figure,

From figure,

∠ QPR = ∠ APB = 35^{0}

(Vertically opposite angles)
We know,
Angle subtended by a chord at the centre is equal to twice of the angle subtended at the circumference of the circle.