Question

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that PQ=12 cm. Fin length of OQ​

Answer 1

Answer:

the length of OQ is 13 cm.

I think you got it

Answer 2

Given:

✰ A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q.

✰ PQ = 12 cm

To find:

✠ The length of OQ.

Solution:

Here in this question, we will use Pythagoras theorem to find the length of OQ.

Refer the figure in thr attachment. O is the centre of the circle. PQ is the tangent drawn to the circle.

Radius of a circle i.e, OP = 5 cm

PQ = 12 cm

OP is perpendicular to the tangent PQ,

⤳OP ⟂ PQ

The tangent meets the circle at point P. So, the tangent at any point of a circle is perpendicular to the radius of a circle of contact i.e, ∆OPQ forms a right-angled triangle.

∠OPQ= 90°

In ∆OPQ, which is a right-angled triangle.

By using Pythagoras theorem, we have:

➛ H² = P² + B²

➛ OQ² = OP² + PQ²

➛ OQ² = 5² + 12²

➛ OQ² = 25 + 144

➛ OQ² = 169

➛ OQ = √169

➛ OQ = 13 cm

∴ The length of OQ = 13 cm

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