Math, asked by tinkuacharya14, 8 months ago

PQ is a common tangent of two circles that touches the two circles at point A and B respectively . prove that extended AB bisects PQ.?​

Answers

Answered by dp14380dinesh
2

Let PQ be the common tangent through P, where Q is the point that meets AB

Now, QA=QP (Tangents to the circle from the same point)

QP=QB (Tangents to the circle from the same point)

Thus, QA=QP=QB

Thus, Points A,B,P lie on the circle with centre Q and AB as the diameter.

Thus, ∠APB=90

(Angle in a semi-circle)

Answered by 4trinasen
0

Answer:

Let PQ be the common tangent through P, where Q is the point that meets AB

Now, QA=QP (Tangents to the circle from the same point)

QP=QB (Tangents to the circle from the same point)

Thus, QA=QP=QB

Thus, Points A,B,P lie on the circle with centre Q and AB as the diameter.  

Thus, ∠APB=90  

 (Angle in a semi-circle)

Step-by-step explanation:

Let PQ be the common tangent through P, where Q is the point that meets AB

Now, QA=QP (Tangents to the circle from the same point)

QP=QB (Tangents to the circle from the same point)

Thus, QA=QP=QB

Thus, Points A,B,P lie on the circle with centre Q and AB as the diameter.  

Thus, ∠APB=90  

 (Angle in a semi-circle)

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