Question

Two circles touch each other at point C. prove that the common tangent to circle at C bisects the common tangents at P and Q

Answer 1


Let PQ and RS are two direct common tangents and EF is the transverse common tangent.

We know that tangent line segments are equal in length from an external point to circle.  

Therefore, EP = EC and EQ = EC ⇒ EP = EQ

and FR = FC, FS = FC ⇒  FR = FS  

Hence, ECF bisects PQ and ECF bisects RS.

∴ The common tangent bisects the other two common 

Answer 2

Answer:

Two circles touch each other at point C. prove that the common tangent to circle at C bisects the common tangents at P and Q

Step-by-step explanation: