Question

If the length of a tangents to a circle from a point is $0.5cm$ and distance of a point from its centre is $1.5cm$, then find its radius.

Answer 1

Given

$OA=1.5$

$AB=0.5$

We know tangent makes ${90}^o$ with center

$\therefore O{A}^2=A{B}^2+O{B}^2$

${1.5}^2={0.5}^2+O{B}^2$

$2.25=0.25+O{B}^2$

$2=O{B}^2$

$OB=\sqrt{2}$.