Question

Prove that the line segment joining the points of contact of two parallel tangents to a circle is a diameter of the circle.​

Answer 1

Step-by-step explanation:

DRAW ACIRCLE OF CENTER O

WE KNOW THAT THE ANGLE AT POINT OF CONTACT IS 90DEGREES

AS PER THEROEM 9.1 THAT WE HAVE IS,

THE LINE IS THE RADIUS OF THE CIRCLE.

THEN IF WE JOIN TWO RADII, IT WILL BECOME A DIAMETER

Answer 2

Answer:

Step-by-step explanation

Given:

l and m are the tangent to a circle such that l || m, intersecting at A and B respectively.

To prove :

AB is a diameter of the

circle .

Proof:

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

∴ ∠XAO = 90°

and ∠YBO = 90°

Since ;

∠XAO + ∠YBO = 180°

Angle on the same side of the

transversal is 180°. Hence ,

the line AB passes through the centre and is the diametet of the circle.