Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre

Solution:

Let's draw a tangent PQ to a circle as shown below.

As we know that, a tangent at any point of a circle is perpendicular to the radius through the point of contact.

At the point of contact P, RP is perpendicular to the tangent PQ.

We also know that the radius or diameter will always pass through the centre of the circle.

Therefore, PR passes through the centre O.

Hence it is proved that perpendicular PR of tangent PQ passes through centre O.

☛ Check: NCERT Solutions Class 10 Maths Chapter 10

Video Solution:

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre

Maths NCERT Solutions Class 10 Chapter 10 Exercise 10.2 Question 5

Summary:

It is proved that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

☛ Related Questions:

• 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(A) 7 cm(B) 12 cm(C) 15 cm(D) 24.5 cm
• In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that ∠ POQ = 110°, then ∠ PTQ is equal to(A) 60°(B) 70°(C) 80°(D) 90°
• If tangents PA and PB from a point P to a circle with center O are inclined to each other at angle of 80°, then ∠POA is equal to(A) 50°(B) 60°(C) 70°(D) 80°
• Prove that the tangents drawn at the ends of a diameter of a circle are parallel.