Question

If P and R are the centres of their respective circles, then what will be the measure of angle SPQ?​

Answer 1

Given:

Two circles are given which passes each other at the center.

To find:

∠SPQ.

Step-by-step explanation:

Step 1 of 2

The given two circles crosses each other at the center.

They both have the same radius as it is clear from the circle.

Now we will join PQ, QR, RS, and SP.

PS = SR = PR              (radii of circle 1 and 2 are equal)

And PQ = QR = RS.

The ΔPSR and ΔPQR are equilateral triangles.

Step 2 of 2

∠SPR = ∠PRA = ∠RSP = 60°

∠PQR = ∠QRP = ∠RPQ = 60°

∠SPQ = ∠SPR + ∠RPQ

∠SPQ = 60° + 60°

∠SPQ = 120°