In the following figure, point ‘A’ is the centre of the circle. Line MN is tangent at point M. If AN = 10 cm and MN = 5 cm, determine radius of the circle.
Seg AM is the radius and line MN is the tangent to the circle at the point M.
`:. angleAMN = 90^@` .....(Tangent is perpendicular to the radius)
In right-angled `triangle AMN` , by Pythagoras’ theorem
`AN^2 = AM^2 + MN^2`
`:.(10)^2 =AM^2 + (5)^2`
`:. AM^2 = (10)^2 - (5)^2 = 100 - 25 = 75`
`:.AM = sqrt75 = sqrt(25xx3)`
`:.AM = 5sqrt3`cm
The radius of the circle is `5sqrt3`cm.