MathematicsIn the given figure, O is the center of the circle. The measure of ∠CBD   will be ____o.

In the given figure, O is the center of the circle. The measure of CBD   will be ____o.


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    Solution:

    In the given figure, O is the center of the circle. The measure of CBD   will be 50o.
    It is given that both angles APC   and AOC   are subtended by the points A and C.
    We know that the angle subtended by the arc to the center of the circle is double the angle subtended by it to the point on the circle.
    AOC =2APC APC = 1 2 × 100 ° APC = 50 °              ...(i)
    ABC   and APC  are opposite angles of the cyclic quadrilateral APCB, which are supplementary.
    APC+ABC = 180 ° ABC = 180 ° APC ABC = 180 ° 50 ° ABC = 130 °   …..(ii)
    ABC  and CBD   form a straight angle.
    CBD+ABC = 180 ° CBD = 180 ° ABC CBD = 180 ° 130 ° CBD = 50 °  
    Therefore, the required answer is 50o.
     
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