The
lengths of the two tangents segments to a circle drawn from an external point
are equal.
Given:
Seg PA and seg PB are tangents.
To
Prove: Tangent PA ≅ Tangent PB
Solution:
|
In ∆ AOP and ∆ BOP,
|
∠ A = ∠
B = 900 [∵ Radius is perpendicular to the
tangent]
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∴ Hypotenuse OP ≅ Hypotenuse OP [ common side]
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Side OA ≅ Side OB [Radii of same circle]
|
∴ ∆ AOP ≅ ∆ BOP [ By
Hypotenuse side test for congruency]
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∴ Tangent PA ≅ Tangent PB
[C.S.C.T.]
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