Question

the length of tangent drawn to circle of radius 5cm is 12CM , then the distance of external point to the centre of circle is​

Answer 1

Given:-

• Radius of Circle = 5 cm

• Length of Tangent = 12 cm

To Find:-

• Distance of external point to the centre of circle.

Theorem Used :-

• The Radius of the Circle is perpendicular to the Tangent at the point of contact on Circle.

• Pythagoras Theorem

Solution:-

As we know,

The Radius is perpendicular to the Tangent. So, it will form a right angled triangle.

Applying Pythagoras Theorem,

$\sf :\implies\:H^2 = P^2 + B^2$

Here,

• Perpendicular = 5 cm

• Base = 12 cm

Putting Values,

$\sf :\implies\:H^2 = P^2 + B^2$

$\sf :\implies\:H^2 = 5^2 + 12^2$

$\sf :\implies\:H^2 = 25 + 144$

$\sf :\implies\:H^2 = 169$

$\sf :\implies\:H = \sqrt{169}$

$\sf :\implies\:H = 13\:cm$

Hence, The distance of external point to the centre of circle is 13 cm.

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