Prove the length of a tangent from an external point to a circle are equal
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PLS MARK AS BRAINALIST
PLS MARK AS BRAINALIST
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Theorem : The lengths of tangents drawn from an external point to a circle are equal.
Given : A circle with centre O. P is a point Lyon outside the circle and PA and PB are two tangents.
Required To Prove : PA = PB
Proof :
Join OA,OB and OP
∠OAP = ∠OBP = 90° [angle between tangent and radii is 90°]
In ∆OAP, ∠A = 90° and in ∆OBP,∠B = 90°
OA = OB [radii of circle]
OP = OP [common side]
∠A = ∠B = 90°
∆OAP ≈ ∆OBP [RHS congruency]
PA = PB [CPCT]
Hence proved.
Given : A circle with centre O. P is a point Lyon outside the circle and PA and PB are two tangents.
Required To Prove : PA = PB
Proof :
Join OA,OB and OP
∠OAP = ∠OBP = 90° [angle between tangent and radii is 90°]
In ∆OAP, ∠A = 90° and in ∆OBP,∠B = 90°
OA = OB [radii of circle]
OP = OP [common side]
∠A = ∠B = 90°
∆OAP ≈ ∆OBP [RHS congruency]
PA = PB [CPCT]
Hence proved.
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