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Question
In the given figure, PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA ⊥ PB, then the length of each tangent is
(a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm
In the given figure, PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA ⊥ PB, then the length of each tangent is
(a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm
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Solution
given PA and PB are two tangents. PA is perpendicular to PB.
in triangles PAO and PBO,
PA= PB [tangents drawn from external point are equal in length]
OP is common.
OA= OB = radius
therefore by SSS triangles are congruent.
∠APO=∠BPO = 90/2=45
in right angled triangle OAP,
∠APO = ∠AOP = (180-90)/2=45
PA = OA = 4 cm
therefore the length of the tangent is 4 cm
Correct option is (b) 4cm
given PA and PB are two tangents. PA is perpendicular to PB.
in triangles PAO and PBO,
PA= PB [tangents drawn from external point are equal in length]
OP is common.
OA= OB = radius
therefore by SSS triangles are congruent.
∠APO=∠BPO = 90/2=45
in right angled triangle OAP,
∠APO = ∠AOP = (180-90)/2=45
PA = OA = 4 cm
therefore the length of the tangent is 4 cm
Correct option is (b) 4cm
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