KnowledgeBoat Logo

Mathematics

From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is

  1. 7 cm

  2. 12 cm

  3. 15 cm

  4. 24.5 cm

Circles

2 Likes

Answer

Let P be the point of contact of tangent with the circle and O be the center of the circle.

From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is 1. 7 cm 2. 12 cm 3. 15 cm 4. 24.5 cm. NCERT Class 10 Mathematics CBSE Solutions.

We know that,

The tangent at any point of a circle is perpendicular to the radius through the point of contact.

So,

OP ⊥ PQ

In △OPQ,

By pythagoras theorem,

⇒ OQ2 = OP2 + PQ2

⇒ 252 = OP2 + 242

⇒ 625 = OP2 + 576

⇒ OP2 = 625 - 576

⇒ OP2 = 49

⇒ OP = 49\sqrt{49} = 7 cm.

Hence, Option 1 is the correct option.

Answered By

1 Like

Related Questions