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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.

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, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

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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