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# In the Figure of Question 9; If Ab = Ac Then Prove that Bq = Cq. - Mathematics

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#### Question

In the following figure; If AB = AC then prove that BQ = CQ.

#### Solution

Since, from A, AP and AR are the tangents to the circle
Therefore, AP = AR
Similarly, we can prove that

BP = BQ and CR = CQ
AP + BP + CQ = AR + BQ + CR
(AP + BP) + CQ = (AR + CR) + BQ
AB + CQ = AC + BQ
But AB = AC
Therefore, CQ = BQ or BQ = CQ

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