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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