Solution:
Given,
![\[AB\text{ }=\text{ }15\text{ }cm,\text{ }AC\text{ }=\text{ }7.5\text{ }cm\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-67d27fa270cf9f4876bdd1b9cdb6fb69_l3.png "Rendered by QuickLaTeX.com")
Suppose,the radius of the circle to be
![\[r.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-93e1d7105b95d93c7d0308d6b0d4b51a_l3.png "Rendered by QuickLaTeX.com")
So,
![\[AO\text{ }=\text{ }AC\text{ }+\text{ }OC\text{ }=\text{ }7.5\text{ }+\text{ }r\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-73361280141572766f1f88bc40060796_l3.png "Rendered by QuickLaTeX.com")
In right ∆AOB, we have
![\[A{{O}^{2}}~=\text{ }A{{B}^{2}}~+\text{ }O{{B}^{2~}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2906bcf7a5de277ba3fe3a3a6a8580c9_l3.png "Rendered by QuickLaTeX.com")
[By Pythagoras Theorem]
![\[{{\left( 7.5\text{ }+\text{ }r \right)}^{2~}}=\text{ }{{15}^{2}}~+\text{ }{{r}^{2}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-be3929a2bb8c63f0de7a8348396c5769_l3.png "Rendered by QuickLaTeX.com")
![\[56.25\text{ }+\text{ }{{r}^{2}}~+\text{ }15r\text{ }=\text{ }225\text{ }+\text{ }{{r}^{2}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-00fc2a098e74bf0fe3fe8dac1aef3a92_l3.png "Rendered by QuickLaTeX.com")
![\[15r\text{ }=\text{ }225\text{ }-\text{ }56.25\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6cacb13fe7be84d968c1521e437c19b1_l3.png "Rendered by QuickLaTeX.com")
![\[r\text{ }=\text{ }168.75/\text{ }15\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e2cbe67c0290f1e16ae55186b65ab82e_l3.png "Rendered by QuickLaTeX.com")
Hence,
![\[r\text{ }=\text{ }11.25\text{ }cm\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-093a95b5a8125486c511c196aabcdd61_l3.png "Rendered by QuickLaTeX.com")
Solution:
Given,
Suppose,the radius of the circle to be
So,
In right ∆AOB, we have
[By Pythagoras Theorem]
Hence,