Question

$\overleftrightarrow{CX}$ is a tangent to a circle with centre A, at a point X. $\overline{AX}$ = 5 cm, CX = 12 cm, AC = ?

• A. 12 cm
• B. 4 cm
• C. 9 cm
• D. 13 cm

Answer 1

The correct option is D

13 cm

CX is tangent to the given circle at point X.

$\therefore AXC={90}^{\circ }$ [$\because$ The tangent at any point of a circle and the radius through this point are perpendicular to each other]

As $\angle AXC={90}^{\circ }$, $\Delta AXC$ is a right-angled triangle, with right angle at X.

In $\Delta AXC$,
Given, AX = 5 cm, CX = 12 cm

$(AX{)}^2+(CX{)}^2=(AC{)}^2$ [Pythagoras theorem]

$5^2+{12}^2=(AC{)}^{2}25+144=(AC{)}^2$
$A{C}^2=169$
$AC=\sqrt{169}$
AC = 13 cm