Question

O is the center of a circle of radius 8 cm. The tangent at a point A on the circle cuts a line through O at B such that AB=5 cm. Find OB.

Answer 1

Now

$\angle OAB={90}^{\circ }$ (as a tangent is perpendicular to a circle's radius)

$\therefore \Delta OAB$ is right angled triangle

$\therefore$ Applying pythogorous theorem,

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

$\therefore O{B}^2=8^2+5^2$

$\therefore O{B}^2=64+25=89$

$\therefore OB=\sqrt{89}cm$

Hence value of $OB$ is $\sqrt{89}cm$