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Two circles touch each other internally. Prove that the tangents drawn to the two circles from any point on the common tangent are equal in length.

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Answer

Let two circles touch each other at point P and T is a point on common tangent as shown in the figure below:

Two circles touch each other internally. Prove that the tangents drawn to the two circles from any point on the common tangent are equal in length. Circles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

As tangents drawn from an external point to a circle are equal in length.

From T, TA and TP are tangents to the circle with centre O'.

TA = TP …..(i)

From T, TB and TP are tangents to the circle with centre O.

TB = TP …..(ii)

From (i) and (ii),

TA = TB.

Hence, proved that tangents drawn to two circles from any point on common tangent are equal in length.

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