Question

If $△ABC$ with unequal sides. $P$ is the set of all points which is equidistant from $B$ and $C$ and $Q$ is the set of all point which is equidistant from sides $AB$ and $AC$. Then $n(P\cap Q)$ equals.

• A. $1$
• B. $2$
• C. $3$
• D. Infinite

Answer 1

Answer: (A)

$1$

Given : $\Delta ABC$ is Scalene.

Now, P is set of points equidistant from B and C. i.e. They lie on the perpendicular bisector of line BC.

and Q is the set of points equidistant from line AB and AC. i.e. they lie on the angle bisector of $\angle A$.

There are infinitely many points on P and Q.

But $n(P\bigcap Q)$ is where the two lines intersect which is only at one point. As shown in figure.

$\therefore n(P\bigcap Q)=1$