Mathematics
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.
A is true, R is false.
A is false, R is true.
Both A and R are true and R is correct reason for A.
Both A and R are true and R is incorrect reason for A.
Answer
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.
Hence, option 3 is the correct option.
Related Questions
For a regular hexagon, inscribing a circle, the length of the side of the hexagon and the radius of the circle are :
equal
not equal
side of hexagon is bigger than the radius of the circle
side of hexagon is smaller than the radius of the circle.
For a regular hexagon inscribed in a circle, the radius of the circle and the length of a side of the hexagon are :
equal
not equal
equal, if hexagon is regular
not equal, if hexagon is regular.
In triangle ABC, ∠A = 35° and ∠C = 55°.
Assertion (A): Circle with AC as diameter will pass through the vertex B.
Reason(R): ∠ABC = 180° - (35° + 55°) = 90° = angle of semi-circle.
A is true, R is false.
A is false, R is true.
Both A and R are true and R is correct reason for A.
Both A and R are true and R is incorrect reason for A.
In ΔABC, PQ is perpendicular bisector of side AB and PR is perpendicular bisector of side BC.
Statement (1): Perpendicular bisector of side AC will pass through point P.
Statement (2): Perpendicular bisectors of sides of a triangle are concurrent.
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.