Question

A circle of diameter 6cm was drawn. From a point outside the circle, the length of the tangent drawn to the circle was found out to be 4cm. The distance between the point and the centre of the circle is ___.

• A. 5cm
• B. 10cm
• C. $2\sqrt{3}$cm
• D. 7 cm

Answer 1

The correct option is A

5cm

The diameter of the circle is 6 cm. So, radius r=3cm.

The length of the tangent is given to be 4 cm. Since the radius and the tangent at the point of contact are perpendicular, the line joining the center of the circle and the point from which tangents are drawn becomes a hypotenuse of the right triangle formed by this line segment with the radius and the tangent.

So by Pythagoras theorem,

$(3{)}^2+(4{)}^2=d^2$

$d^2=9+16$

$d^2=9+16$

$d^2=25$

$d=5$

Hence we find d = 5 cm.