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Question
In the figure Q is the contact point. If
PQ = 12, PR = 8, then PS = ?
Solution
By tangent secant theorem,
PQ2 = PS × PR
122 = PS × 8
PS = `144/8`
PS = 18
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Given: In the figure, point A is in the exterior of the circle with centre P. AB is the tangent segment and secant through A intersects the circle in C and D.
To prove: AB2 = AC × AD
Construction: Draw segments BC and BD.
Write the proof by completing the activity.
Proof: In ΔABC and ΔADB,
∠BAC ≅ ∠DAB .....becuase ______
∠______ ≅ ∠______ ......[Theorem of tangent secant]
∴ ΔABC ∼ ΔADB .......By ______ test
∴ `square/square = square/square` .....[C.S.S.T.]
∴ AB2 = AC × AD
Proved.
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