Two circle touch each other internally. Show that the tangents drawn to the two circles from any point on the common tangent are equal in length.
From Q, QA and QP are two tangents to the circle with centre O
Therefore, QA = QP .......(i)
Similarly, from Q, QB and QP are two tangents to the circle with centre O'
Therefore, QB = QP .......(ii)
From (i) and (ii)
QA = QB
Therefore, tangents QA and QB are equal.
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- Tangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers