Question

In fig. PT is a tangent to the cirlce with centre O. Given OP=>20cm , PT=>16cm, find the radius of the circle​

Answer 1

the radius of circle is 25.61 cm

Answer 2

$\bf\underline{\underline{\green{SOLUTION:-}}}$

QuEsTiOn:

In fig. PT is a tangent to the cirlce with centre O. Given OP=>20cm , PT=>16cm, find the radius of the circle?

Answer:

12cm

We know that:

Radius is always perpendicular to tangent

i.e, OT ⊥ PT

Explanation:

$\green{ \implies \triangle \: OPT \: is \: a \: right \: angled \: triangle }$

$\blue{ \implies where \: OP = hypotenuse}$

$\red{ \implies In \: right \: angled \: triangle, }$

$\green{ \tt \: By \: Pythagoras \: theorem \: , we \: get: }$

$\implies \sf OP^{2} = {PT}^{2} + {OT}^{2}$

$\implies \sf OT^{2} = {OP}^{2} - {PT}^{2}$

$\implies \sf OT^{2} = {20}^{2} - {16}^{2}$

$\implies \sf OT^{2} = 400 - 256$

$\implies \sf OT^{2} = 144$

$\implies \sf OT = \sqrt{144}$

we get:

$\implies \sf OT = 12 cm$

therefore:

$\pink{ \implies 12cm \: is \: the \: radius \: of \: the \: circle }$