Question 72

A, B, C are three points on a circle. The tangent at A meets BC produced at T, $$BTA = 40^\circ, CAT = 44^\circ$$. The angle subtended by BC at the centre of the circle

Solution

$$ < CAT = 44^\circ $$ (given)

$$ < BTA = 40^\circ $$ (given)

$$ < ACT = 180 - 44 - 40 = 96^\circ $$

$$ < CAT = < CBA = 44^\circ $$ (alternate theorem)

$$ < BCA = 180 - 96 = 84 $$

therefore, $$ < BAC = 180 - 84 - 44 = 52^\circ $$

therefore, angle subtended by BC at the centre = $$ 2 \times 52 = 104^\circ $$

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