Solution:
Given,
![\[OS\text{ }=\text{ }5\text{ }cm\text{ }and\text{ }OT\text{ }=\text{ }3\text{ }cm\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7a772fa6624e65428da06def83bba626_l3.png "Rendered by QuickLaTeX.com")
In right triangle
![\[OST\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-38faa46c68ba51dc202a275b72c16680_l3.png "Rendered by QuickLaTeX.com")
, we have
![\[S{{T}^{2}}~=\text{ }O{{S}^{2}}~\text{ }O{{T}^{2}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-721bb19617639dcf7f41eb3ffb49adef_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }25\text{ }-\text{ }9\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0f32fc7e01ad0c791c25074e298636f8_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }16\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7aba7516a87b5523fb1697be6bc231d6_l3.png "Rendered by QuickLaTeX.com")
So,
![\[ST\text{ }=\text{ }4\text{ }cm\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4fccf56902f7dd626e536b7f5b965610_l3.png "Rendered by QuickLaTeX.com")
As we know,
![\[OT\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-59a591d55db782fd49ddd75996423b6e_l3.png "Rendered by QuickLaTeX.com")
is perpendicular to
![\[SP\text{ }and\text{ }OT\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d89888113c885bcd8f4ed35e983c6d72_l3.png "Rendered by QuickLaTeX.com")
bisects chord
![\[~SP\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9598c19620eee2eb26bde0e34cdb514b_l3.png "Rendered by QuickLaTeX.com")
Thus,
![\[SP\text{ }=\text{ }2\text{ }x\text{ }ST\text{ }=\text{ }8\text{ }cm\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-14be1caa47fc54414e29e7053de8aa98_l3.png "Rendered by QuickLaTeX.com")
Solution:
Given,
In right triangle
, we have
So,
As we know,
is perpendicular to
bisects chord
Thus,
