# Thread: [Arcs, sectors and segments] Area intersection problem.

1. ## [Arcs, sectors and segments] Area intersection problem.

EDIT: The picture diagram is rather incorrect as to the scale of 5cm all the way across is incorrect but is infact the distance between the two centers of the circle, apologies for the error.

2. Let P and Q be the centers of the circles. Let Aand B be the points of intersection of the circles.

PA = 3 cm, QA = 4 cm and PQ = 5 cm. So PAQ is a right angled triangle. Find the area of the triangle PAQ.

Find the angles APQ and AQP by using sin(APQ) = AQ/PQ and sin(AQP) = AP/PQ.

Find the area of the sectors formed by the angles APQ and AQP and add them.

Required area = 2[sum of the area of the sectors - area of the right angled triangle]

3. Thanks, that was straight to the point.