Question

8.In the given figure, two circles touch
each other at the point C Prove that the
common tangent to the circles' at C, bisects the
common tangent at Pand Q.
R
P​

Answer 1

Step-by-step explanation:

Question

In the given figure, two circles touch each other at the point C. Prove that the common tangent to the circles at C, bisects the common tangent at P and Q.

Answer

In the given figure, PR and CR are both tangents drawn to the same circle from an external point R.

\(\therefore\) PR = CR. ...(i)

Also, QR and CR are both tangents drawn to the same circle (second circle) from an external point R

QR = CR ... (ii)

From (i) and (ii), we get

PR = QR [each equal to CR].

R is the midpoint of PQ,

i.e., the common tangent to the circles at C, bisects the common tangent at P and Q.

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