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  • Prove that tangents drawn at the ends of a diameter of a circle are parallel.        

Prove that tangents drawn at the ends of a diameter of a circle are parallel.

 

 

 
 
 
 
 

Answers (1)

To prove \rightarrow AB\parallel CD

Given\rightarrow Diameter = PQ

               Centre  = O      

Proof \rightarrow

Theorem \rightarrow Tangent drawn at any point of the circle is perpendicular to the radius through the point of contact.

Now, AB\perp OP (According to the above theorem)

\Rightarrow \angle OPA=90^{o}\; \; \; \; \; \; \; ---(i)

Similarly, CD\perp OQ (According to the above theoram)

\Rightarrow \angle OQD=90^{o}\; \; \; \; \; \; \; ---(ii)

From eq (i) and (ii)

\angle OPA=90^{o}  and \angle OQD=90^{o}

Therefore,

\angle OPA=\angle OQD

Or

\angle OPA=\angle PQD

For lines AB and CD and transversal PQ

\angle OPA=\angle PQD (Both alternate angles are equal)

Hence lines are parallel

\therefore AB\parallel CD

Posted by

Safeer PP

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