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Question
Two circle touch each other externally at point P. Q is a point on the common tangent through P. Prove that the tangents QA and QB are equal.
Solution
From Q, QA and QP are two tangents to the circle with centre O
Therefore, QA = QP ...(i)
Similarly, from Q, QB and QP are two tangents to the circle with centre O'
Therefore, QB = QP ...(ii)
From (i) and (ii)
QA = QB
Therefore, tangents QA and QB are equal.
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