Question

In triangle ABC, bisectors of angles A and B meet at point P.

Assertion (A): PC bisects angle C.

Reason (R): Bisectors of angles of a triangle are concurrent.

Options

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

The point of intersection of the bisectors of angles of a triangle is called the incenter of the triangle.

Thus, we can say that,

Bisectors of angles of a triangle are concurrent.

So, reason (R) is true.

Since, from figure, P is the incenter, so bisector of angle C will pass through it.

Thus, we can say that,

PC bisects angles C.

So, assertion (A) is true.

∴ Both A and R are true and R is correct reason for A.