In a right triangle ABC, a circle with a side AB diameter is drawn to intersect the hypotenuse AC in P. Prove that the tangent to the circle at P bisects the side BC.

Internal bisector of an angle angle A of triangle ABC meets side BC at D. A line drawn through D perpendicular to AD intersects the side AC at E and the side AB at F. If a, b, c represent the sides of DABC then

If the bisector of an angle of a triangle also bisects the opposite side, prove that the triangle is isosceles.

In a right triangle ABC, right angled at B , BC = 15 cm and AB = 8 cm . A circle is inscribed in the traiangle ABC . The radius of the circle is ……

Equilateral triangle are drawn on the three sides of a right angled Triangle. Show that the area of the Triangle on the hypotenuse is equal to the sum of the areas of triangle on the other two sides.

In a triangle ABC, AD is the median drawn on the side BC is produced to E such that AD = ED prove that ABEC is a parallelogram.

In a right angle triangle, length of the hypotenuse is 6 cm more than its shortest side. The length of the other side is 3 cm less than the hypotenuse, then find the sides of right angle triangle.

In acute-angled triangle ABC, AD is the altitude, Circle drawn with AD as its diameter cuts the AB and AC at P and Q, respectively. Length PQ is equal to

P and P' are corresponding points on an ellipse and its auxilliary circle. Prove that the tangents at P and P' intersect on the major axis.