Mathematics
In the figure (ii) given below, two circles touch internally at P from an external point Q on the common tangent at P, two tangents QA and QB are drawn to the two circles. Prove that QA = QB.
Circles
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Answer
From figure,
QA and QP are the tangents to the outer circle.
∴ QA = QP …..(i) (∵ the length of the different tangents to a circle from a single point are equal.)
Similarly, from Q, QB and QP are the tangents to the inner circle.
∴ QB = QP …..(ii) (∵ the length of the different tangents to a circle from a single point are equal.)
From (i) and (ii),
QA = QB.
Hence, proved that QA = QB.
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