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

(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 rectangle 

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.