In the given figure, O is the centre of the circle and AB is a tangent to the circle at B. If AB = 15 cm and AC = 7.5 cm, calculate the radius of the circle. - Noon Academy

In the given figure, O is the centre of the circle and AB is a tangent to the circle at B. If AB = 15 cm and AC = 7.5 cm, calculate the radius of the circle.

Class 10 | Exercise 18A | ICSE | Maths | Selina | Tangents and Intersecting Chords

In the given figure, O is the centre of the circle and AB is a tangent to the circle at B. If AB = 15 cm and AC = 7.5 cm, calculate the radius of the circle.

Selina Solutions Concise Class 10 Maths Chapter 18 ex. 18(A) - 2

Solution:

Given,

$AB\text{ }=\text{ }15\text{ }cm,\text{ }AC\text{ }=\text{ }7.5\text{ }cm$

Suppose,the radius of the circle to be

$r.$

So,

$AO\text{ }=\text{ }AC\text{ }+\text{ }OC\text{ }=\text{ }7.5\text{ }+\text{ }r$

In right ∆AOB, we have

$A{{O}^{2}}~=\text{ }A{{B}^{2}}~+\text{ }O{{B}^{2~}}$

[By Pythagoras Theorem]

${{\left( 7.5\text{ }+\text{ }r \right)}^{2~}}=\text{ }{{15}^{2}}~+\text{ }{{r}^{2}}$

$56.25\text{ }+\text{ }{{r}^{2}}~+\text{ }15r\text{ }=\text{ }225\text{ }+\text{ }{{r}^{2}}$

$15r\text{ }=\text{ }225\text{ }-\text{ }56.25$

$r\text{ }=\text{ }168.75/\text{ }15$

Hence,

$r\text{ }=\text{ }11.25\text{ }cm$

i

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