Question

The length of the tangent from a point A to a circle of radius 9 cm is 12 cm. find the distance of A from the centre of the circle

Answer 1

Step-by-step explanation:

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Answer 2

The distance of A from the centre of the circle is 15 cm.

Explanation:

We know that the tangent makes right angle with the radius of the circle , therefore the the triangle made by tangent from point A , radius and the line segment that joins the center and the point A would be a right triangle , where the joins the center and the point A would be the hypotenuse ( ∵ it is the opposite side to right angle.)

Let d be the distance of A from the centre of the circle.

By Pythagoras theorem of right triangle  , we have

$d^2=9^2+12^2\\\\ d^2=81+144\\\\ d^2=225\\\\ d=\sqrt{225}=15$

Hence, the distance of A from the centre of the circle is 15 cm.

# Learn more :

Prove that the lengths of the tangents from an external point to a circle are equal.

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