Fig. 9.39, two circles touch each otherrnally at C. Prove that the com

1.	Fig. 9.39, two circles touch each otherrnally at C. Prove that the common tangentbisects, the other two common tangents.(C.B.S.E. 2007)
Answer» 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 tangents

Fig. 9.39, two circles touch each otherrnally at C. Prove that the common tangentbisects, the other two common tangents.(C.B.S.E. 2007)

Answer»

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 tangents