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Question

ABC is an isosceles triangle in which AB = AC, circumscribed about a circle. Show that BC is bisected at the point of contact.  [1 MARK]


Solution

Concept: 1 Mark

Given that AB = AC

BP + AP = CR + RA   ….(i)

But the lengths of tangents drawn from an external point to a circle are equal.

AP = RA

Equation (i) becomes

BP = CR    …..(ii)

Now BP = BQ and CQ = CR

Now (ii) becomes

BQ = CQ

Therefore BC is bisected by the circle at Q.

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