Question

Line AB intersects circle c at points a and b, as shown, and is 12 cm long. If line AB is 2cm from the center of the circle c, what is the radius of circle c to the nearest tenth of a centimeter.

Answer 1

The radius of circle with center c is 6.3 cm

Explanation:

Given as :

For a circle , The line AB intersects circle at a , b

The length of AB = 12 cm

The distance of AB from the center of circle c = 2 cm

Let The radius of circle = r cm

Now ,

Since , AB intercept on circle , so the length from center divide the intercept equally I.e AD = DB = 6 cm. and the length will make right angle on AB

So, radius from center c to the point b is r

∴ r = BD + cD

Or, r² = BD² + cD²

Or, r² = 6² + 2²

Or, r² = 36 + 4

Or, r² = 40

∴ r =
`√(40)` = 6.324 cm

I,e r = 6.3 cm

Hence The radius of circle with center c is 6.3 cm Answer