Question

$AB$ and $AC$ are tangents to the circle with centre $O.$ Then $x$ equals.

• A. ${22}^{\circ }$
• B. ${18}^{\circ }$
• C. ${20}^{\circ }$
• D. ${36}^{\circ }$

Answer 1

Answer: (B)

${18}^{\circ }$

In $△AOB$ and $△AOC$
$AB=AC$ (Tangents from the same point on the circle)
$OB=OC$ (radius of the circle)
$AO=AO$ (Common)
Thus, $△AOB\cong △AOC$ (S-A-S rule)
$\angle BOA=\angle COA={72}^{\circ }$
Now, in $△AOC$
Sum of angles $={180}^{\circ }$
$\angle AOC+\angle COA+\angle ACO={180}^{\circ }$
$x+{72}^{\circ }+{90}^{\circ }={180}^{\circ }$ ($\angle OCA={90}^{\circ }$, angle between radius an the tangent)
$x={18}^{\circ }$