Question

find the length of tangent segment drawn to a circle with radius 5cm from a point 13cm from the centre of the circle​

Answer 1

SOLUTION:-

Given:

•Radius= 5cm

• A point 13cm from the centre of the circle.

To find:

The length of tangent segment.

Explanation:

•Firstly, draw a circle which center O.

•OP= radius= 5cm

•A tangent drawn at point P, such that line through O intersects at Q.

•OB= 13cm.

In right ∆OPQ,

Using Pythagoras Theorem:

(Hypotenuse)²=(base)²+(perpendicular)²

=) OQ²= OP² + PQ²

=) 13² = 5² + PQ²

=) 169= 25 + PQ²

=) PQ² = 169 -25

=) PQ² = 144

=) PQ= √144

=) PQ = 12cm

Thus,

The length of the tangent drawn is 12cm.

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Answer 2

Answer:

We join OT which is a radius .

∴ OT =5 cm.

Now ∠OAT=90

since the angle between a tangent to a circle and the radius joining the centre and the point of contact =90

.

∴Δ OAT is a right one with OA as hypotenuse.

So, applying Pythagoras theorem, we have AT= OA

2−OT 2

= 13

2−5

2cm=12cm.

Ans- Option A.