Question

Given the length of tangent and the distance of external point from the centre, match the corresponding radii.

• A. 9 cm
• B. 7 cm
• C. 8 cm
• D. 5 cm

Answer 1

Consider the case where length of the tangent from a point outside the circle is 12 cm and distance of point from centre is 15 cm.
The radius from the point of contact, the tangent and the line segment from the centre to the external point form a right angle triangle.
So by Pythagoras theorem,

$(12{)}^2+(r{)}^2=(15{)}^2$.

$r^2=225-144=81$
$r=9$
Hence, the radius, in this case, must be 9 cm.

Similary, when length of the tangent from a point outside the circle is 24 cm and the distance of the point from the centre is 25 cm.
$r^2+{24}^2={25}^2$
$r^2+576=625$
$r^2=49$
$r=7cm$

Similary, when length of the tangent from a point outside the circle is 15 cm and the distance of the point from the centre is 17 cm.
$r^2+{15}^2={17}^2$
$r^2+225=289$
$r^2=64$
$r=8cm$

Similary, when length of the tangent from a point outside the circle is 12 cm and the distance of the point from the centre is 13 cm.
$r^2+{12}^2={13}^2$
$r^2+144=169$
$r^2=25$
$r=5cm$