Question

find the length of tangent from a point M which is at the distance of 17cm from the centre of the circle of radius is 8 cm find the length
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Answer 1

Answer:

Since, MN is the tangent of the circle,

∠MNO = 90⁰

⟹ MO² = MN² + ON²

⟹ 17² = MN² + 8²

⟹ 289 = MN² + 64

⟹ 289 – 64 = MN²

⟹ MN² = 225

⟹ MN = 15

Thus the length of the tangent is 15 cm.

Step-by-step explanation:

Let, radius of the circle be r cm.

We know, any tangent to a circle is perpendicular to the radius passing through that touch-point.

So, here it is a case of right angled triangle having perpendicular sides of r cm and 8 cm; while hypotenuse is of 17 cm.

So, 17^2 = r^2 + 8^2

r^2 = 289 - 64 = 225

r = 15.

Radius of the circle = 15 cm.