Question

P is the centre of two concentric circles having radius 3 cm and 5 cm. Two tangents are drawn from point A which is outside the circle. Tangent AM touches the smaller circle at point M and tangent AN touches the bigger circle at point at point N. If AM = 13 cm then AN =?​

Answer 1

Answer:

We know Radius and tangent are perpendicular at the point of contact.

So angle ∠PMA = angle ∠PNA = 90 degree

PM = 3cm and PN = 5 cm

AM= 13cm

So Δ PMA , ∠ M= 90 degree

So by Pythagoras theorem

PA²  =  PM² + AM²

         3² + 13²

PA²       =  9 + 169= 178

Now in Δ PNA, ∠N = 90

so PA² = PN² +AN²

  178  =  5² + AN²

AN² =  178 - 25

        =  153

AN = √153

Step-by-step explanation: