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Question
In the given figure, the chord AB of the larger of the two concentric circles, with center O, touches the smaller circle at C. Prove that AC = CB.
Solution
Construction: Join OA, OC and OB
We know that the radius and tangent are perpendicular at their point of contact
∴ ∠OCA = ∠OCB = 90°
Now, In Δ OCA and ΔOCB
∠OCA = ∠OCB = 90°
OA = OB (Radii of the larger circle)
OC = OC (Common)
By RHS congruency
Δ OCA ≅ Δ OCB
∴ CA =CB
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