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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. - Geometry

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.

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Solution

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.

Concept: Theorem - Converse of Tangent at Any Point to the Circle is Perpendicular to the Radius
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