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From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is : 

(a) 60 cm

(b) 65 cm2 

(c) 30 cm2 

(d) 32.5 cm2

1 Answer

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Best answer

(a) 60 cm2

The radius ⊥ tangent at the pt. of contact, 

therefore, OQ ⊥ PQ and OR ⊥ PR

∴ In rt. ΔΟPQ,

PQ = \(\sqrt{OP^2-OQ^2}\)

\(\sqrt{169-25}\)

\(\sqrt{144}\) = 12 cm

\(\Rightarrow\) PR = 12 cm (Two tangents from the same external pt. to a circle are equal) 

Now area of quad. PQOR = 2 × Area of ΔPΟQ

= (2 x \(\frac{1}{2}\) x 12 x 5) cm= 60 cm2

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