Mathematics
Two circles touch each other externally at a point C and P is a point on the common tangent at C. If PA and PB are tangents to the two circles, prove that PA = PB.
Answer
The tangents from a point outside the circle are equal.
The point P is also external to the right circle. The segments PB and PC are tangents drawn from P to this circle.
PB = PC ………(1)
The point P is external to the left circle. The segments PA and PC are tangents drawn from P to this circle.
PA = PC ………(2)
From (1) and (2), we get :
∴ PA = PB.
Hence, proved that PA = PB.
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