Question

22) The length of tangents drawn from

an external point to a circle are equal to
4 cm and radius is 3 cm then the
distance of external point from the
centre is
O 2 cm
O 3 cm
O 4 cm
O 5 cm

Answer 1

The length from the external point to the center of the circle is 5 cm

Explanation:

Here, we want to calculate the distance from the center of the circle to the external point

Please check attachment for diagram

Now, from what we know, the tangent and the radius meets at right angle

So we have a right-angled triangle with the length from the external point to the center of the circle as hypotenuse;

While the radius and the length of the tangent to the circle as the other sides

Using Pythagoras’ theorem, the square of the hypotenuse equals the sum of the squares of the two other sides

Let the length we want to calculate be x

x^2 = 3^2 + 4^2

x^2 = 9 + 16

x^2 = 25

x = √25

x = 5 cm