Question

Match the statements in Column I with the properties in Column II:

Column I		Column II
A	Two intersecting circles	P	have a common tangent.
B	Two mutually external circles	Q	have a common normal.
C	Two circles, on strictly inside the other	R	do not have a common tangent.
D	Two branches of a hyperbola	S	do not have a common normal.

• A. $(A)\to (P),(Q);(B)\to (P),(Q);(C)\to (Q),(R);(D)\to (Q)(R)$
• B. $(A)\to (R),(S);(B)\to (P),(Q);(C)\to (Q),(R);(D)\to (P)(R)$
• C. $(A)\to (P),(R);(B)\to (P),(Q);(C)\to (Q),(R);(D)\to (Q),(R)$
• D. $(A)\to (P),(S);(B)\to (P),(Q);(C)\to (Q),(R);(D)\to (P),(R)$

Answer 1

Answer: (A)

$(A)\to (P),(Q)$
When two circles are intersecting, they have a common normal and common tangent.
(B) $\to (P),(Q)$
Two mutually external circles have a common normal and the common tangents.
(C) $\to$ (Q), (R)
When one circle lies inside of the other, then they have a common normal but they do not have common tangents.
(D) $\to (Q),(R)$
Two branches of a hyperbola have a common normal but they do not have common tangents.