Question

In the given figure 'O' is the centre of the circle and AB is tangent at B. If AB = 15 cm and AC = 7.5 cm. Calculate the diameter of the circle (in cm). [2 marks]

Answer 1

$\angle$OBA = ${90}^{\circ }$ [By Theorem- The tangent at any point of a circle is perpendicular to the radius through the point of contact]

Applying pythagoras theorem in right angled $△$ ABO
$\Rightarrow$${OB}^2$ = ${OA}^2$ - ${AB}^2$
$r^2$ = ${(r+7.5)}^2$ - ${15}^2$
$r^2$ = $r^2$ + 56.25 + 15$r$ - 225
15$r$ = 168.75
$r$ = $\frac{168.75}{15}$
$r$ = 11.25 cm
$\therefore$ Diameter = 2$r$ = 2$\times$11.25 = 22.5 cm
(2 marks)