Mathematics
In the given figure, if AB = AC then prove that BQ = CQ.
Circles
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Answer
As, from point A, AP and AR are the tangents to the circle.
We know that,
If two tangents are drawn to a circle from an exterior point, the tangents are equal in length.
So, we have AP = AR ……….(1)
From point B, BP and BQ are the tangents to the circle.
∴ BP = BQ ……….(2)
From point C, CQ and CR are the tangents to the circle.
∴ CQ = CR …………(3)
Adding equations (1), (2) and (3), we get :
⇒ AP + BP + CQ = AR + BQ + CR
⇒ (AP + BP) + CQ = (AR + CR) + BQ
⇒ AB + CQ = AC + BQ
Given,
AB = AC
∴ BQ = CQ.
Hence, proved that BQ = CQ.
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