Question

Prove that the line segment joining the point of contact of two parallel tangent of a circle passes through its centre

Answer 1

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...


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Answer 2

Answer:

Step-by-step explanation:

“Consider AB and CD are two parallel tangents to the circle. “ 

“Consider P and Q be the point of contact and POQ be a line segment.”

“Construction: Join OP and OQ where O is the centre of a circle.”

“Proof:  OQ ⊥CD and OP ⊥ AB.”

“Since AB || CD, OP || OQ.”

“As OP and OQ pass through O,” 

“Hence,  POQ is a straight line which passes through the tangent of a circle