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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 


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


Mathematics
Secondary School Mathematics X
Standard X

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