Mathematics
In the given figure, AP is bisector of angle A of △ ABC and DP is perpendicular bisector of side AB, then :
P is incenter of △ ABC
P is circumcenter of △ ABC
PB bisects angle B
none of these
Answer
The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle.
The circumcenter of a triangle is defined as the point where the perpendicular bisectors of the sides of triangle intersect.
Since,
In the given figure, P is intersection of an angle bisector and perpendicular bisector of a side.
Hence, Option 4 is the correct option.
Related Questions
Incenter of a triangle is the point of intersection of the :
perpendicular bisector of its sides
bisectors of its angles
one perpendicular of its side and bisector of any one angle of it
none of these.
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.
A regular octagon is circumscribing a circle, the angle subtended by each side of the regular octagon at the center of the circle is :
60°
30°
45°
(2 × 8 - 4) × 90°