Question

Calculate the length of tangents from a point 15cm away from the centre of a circle of radius 9cm.

Answer 1

Answer:

12 cm

Step-by-step explanation:

The radius, tangent and the line joining the point and centre of the circle form a right angled triangle.

In the triangle,

the line joining the point and centre of the circle = hypotenuse = 15cm

radius = perpendicular = 9cm

tangent = base = b

using pythagoras theorem,

$h^2 = p^2 + b^2\\ \\ \Rightarrow 15^2 = 9^2 + b^2\\ \\ \Rightarrow 225 = 81 + b^2\\ \\ \Rightarrow b^2 = 225-81 = 144\\ \\ \Rightarrow b=\sqrt{144}\\ \\ \Rightarrow b=12\ cm$

Hence length of tangents is 12cm

Answer 2

Answer:

Step-by-step explanation: