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.
Answer
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 …..(1)
From T, TB and TP are tangents to the circle with centre O'.
TB = TP ……..(2)
From (1) and (2),
TA = TB.
Hence, proved that tangents drawn to two circles from any point on common tangent are equal in length.
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