Question

Find the length of the tangent from a point M which is at a distance of 17 cm from the centre O of the circle of radius 8 cm.​

Answer 1

Consider the figure:

Since, MN is the tangent of the circle,

∠MNO = 90⁰

⟹ MO^2 = MN^2 + ON^2

⟹ 172 = MN^2 + 82

⟹ 289 = MN^2 + 64

⟹ 289 – 64 = MN^2

⟹ MN^2 = 225

⟹ MN = 15

Thus, the length of the tangent is 15 cm.

Answer 2

Answer:

From the Given data

OM = 17 cm

OQ = 8cm

$mq = \sqrt{ {17}^{2} + {8}^{2} }$

MQ = 15 cm