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

Answer 1

Answer: (A)

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