Question

A and b are the center of the two circle.Pqr common tangent.Points a,b,c lies on straight line and distance between p and q is 24m.Diameter of the larger circle is 24m.What is the ratio of area of triangle apr and bpr

Answer 1

this is example
Two circles touch each other at point C. Prove that the common tangent to the circles at C, bisects the common tangent P & Q

We know that tangents drawn from an external point to a circle are equal in length.

So, PA = PC  and  PB = PC

⇒PA = PB  so, P is the mid point of AB

Similarly, DQ = QC and QE = QC

⇒DQ = QE so, Q is the mid point of DE.

Thus, the common tangent at point C bisects the common tangents at P and Q. 

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