Mathematics
A point is equidistant from the sides of an obtuse angle triangle. The point is called :
circumcenter of the triangle.
incenter of the triangle.
centroid of the triangle.
orthocenter of the triangle.
Answer
Let ABC be the obtuse triangle.
Steps of construction :
Draw angle bisectors AX, BY and CZ of the interior angles A, B and C of a triangle.
Let the angle bisectors meet at point I.
We know that,
Locus of a point equidistant from two intersecting lines is the bisector of the angles between the lines.
∴ BY is equidistant from AB and BC
∴ AX is equidistant from AB and AC
∴ CZ is equidistant from AC and BC
∴ The point (incenter) joining AX, BY and CZ will be equidistant from all the three sides of the triangle.
Hence, Option 2 is the correct option.
Related Questions
Three isosceles triangles PBC, QBC and RBC are on the same base, then :
P, Q and R are collinear.
△PQR is isosceles triangle.
Q lies on the circumference of a circle with BC as diameter.
Q is mid-point of line segment PR.
Locus of the centers of the circles passing through two fixed points A and B is :
a line parallel to line segment AB.
the bisector of the line segment AB.
perpendicular to line segment AB.
perpendicular bisector of line segment AB.
ABC is a triangle. Point P moves with vertex B as center and radius 2.8 cm. The locus of point P is :
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circle with center at point B and radius = 2.8 cm.
perpendicular bisector of BC.
Draw an ∠ABC = 60°, having AB = 4.6 cm and BC = 5 cm. Find a point P equidistant from AB and BC; and also equidistant from A and B.