Question

The length of the tangent from a point A to a circle, of radius 3 cm, is 4 cm. Find the distance of A from the center of the circle.

• A. $\sqrt{7}$ cm
• B. 7 cm
• C. 5 cm
• D. 25 cm

Answer 1

The correct option is C

5 cm

Given that AB is a tangent, AB = 4 cm and OB = 3 cm.

We know that line joining point of contact of tangent to centre of circle is perpendicular to tangent.
Hence OB $\perp$ BA.

Consider $△OAB$,
${OB}^2$ + ${AB}^2$ = ${OA}^2$
[Applying Pythagoras theorem]
$3^2+4^2=(OA{)}^2$
$(OA{)}^2=25$
OA = 5 cm
Therefore, the distance of A from the center of the circle is 5 cm.