Question

In the given figure, DE and DF are tangents from an external point D to a circle with centre A. If DE = 5 cm and DE ⊥ DF then the radius of the circle is

(a) 3 cm 

(b) 4 cm 

(c) 5 cm 

(d) 6 cm

Answer 1

Correct answer is (c) 5 cm

Construction: Join AF and AE

We know that the radius and tangent are perpendicular at their point of contact

∴ ∠AED = ∠AFD = 90°

Since, in quadrilateral AEDF all the angles are right angles

∴ AEDF is a rectangleis

Now, we know that the pair of opposite sides is equal in rectangle

∴ AF = DE = 5 cm

Therefore, the radius of the circle is 5 cm