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Math Help - [Arcs, sectors and segments] Area intersection problem.

  1. #1
    Junior Member Cthul's Avatar
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    [Arcs, sectors and segments] Area intersection problem.


    I don't know how to do this, please help on steps how to solve this.
    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.
    Last edited by Cthul; July 19th 2010 at 02:53 AM.
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  2. #2
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    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]
    Last edited by sa-ri-ga-ma; July 19th 2010 at 03:24 AM.
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  3. #3
    Junior Member Cthul's Avatar
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    Thanks, that was straight to the point.
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