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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. - Mathematics

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Question

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.

Solution

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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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 18: Tangents and Intersecting Chords
Exercise 18 (A) | Q: 4 | Page no. 274
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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. Concept: Tangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers.
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