Mathematics
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
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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:
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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