Question

The figure shows two circles with radii 3 cm, centred at P and Q respectively. The length of the line segment PQ is 4 cm. R and S are two points on PQ.

(a) Find the length of RS. (b) If the two circles intersect at A and B, are both APQ and BPQ isosceles triangles? Explain your answer.​

Answer 1

Part (a)

Note that PQ is equal to PS + QR - RS. Since PQ is 4 cm and PS and QR are both radii (3 cm each), then this means 4=6-RS, and thus RS = 2 cm.

Part (b)

Yes, because PA, QA, PB, and QB are all radii of congruent circles, and thus all have the same length. This means triangles APQ and BPQ both have two equal sides, and thus isosceles.