In the given figure, two circles touch each other at a point C. Prove that the common tangent to the circles at C bisects the common tangent at the points P and Q.
Answer:
- We see that PR and CR are the tangents drawn from an external point R on the circle with center A.
Thus, PR=CR …(i)
Also, QR and CR are the tangents drawn from an external point R on the circle with center B.
Thus, QR=CR …(ii) - From eq (i) and eq (ii), we get
PR=QR [Both are equal to CR]
Therefore, R is the midpoint of PQ. - Thus, we can say that the common tangent to the circles at C bisects the common tangent at the points P and Q.