Mathematics
In the given figure, two circles intersect each other at the points A and B. If PQ and PR are tangents to these circles from a point P on AB produced, show that PQ = PR.
Circles
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Answer
We know that,
If a chord and a tangent intersect externally, then the product of lengths of the segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.
For circle 1:
∴ PQ2 = PA × PB
For circle 2:
∴ PR2 = PA × PB
Thus,
PQ2 = PR2
Taking square root on both sides,
PQ = PR
Hence, proved that PQ = PR.
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