Question

In the figure below, it is given that chords AB = PQ. The $\angle AOB={55}^0$, and $\angle POQ=x^0$, find $x$.

• A. 55
• B. 25
• C. 35
• D. 45

Answer 1

The correct option is A

55

Here we are given that AB = PQ

Now let us consider $\Delta AOB$ and $\Delta POQ$,

Here, AB = PQ (given)

AO = PO = radius of the circle

Similarly, BO = QO = radius of the circle

$\therefore \Delta AOB\cong \Delta POQ$ (By SSS congruency)

Hence, $\angle POQ={55}^{\circ }$. (C.P.C.T)

Alternate method:

Equal chords subtend equal angles at the centre.

Hence $\angle AOB=\angle POQ={55}^{\circ }$