I is the incentre of the `Delta ABC`. The perpendicular drawn from I to BC intersects BC at. P. Prove that ` AB-AC=BP-CP`.

P is any point on BC of the square ABCD. The perpendicular , drawn from B to AP intersects DC at Q . Prove that AP = BQ.

In DeltaABC , the bisector of /_ABC intersects AC at the point P . Prove that CB: BA=CP:PA .

Let ABC be a triangle with incentre I. If P and Q are the feet of the perpendiculars from A to BI and CI, respectively, then prove that (AP)/(BI) + (AQ)/(Cl) = cot.(A)/(2)

O is the circumcentre of Delta ABC and OD is perpendicular on the side BC, prove that angle BOD= angle BAC

If h be the length of the perpendicular drawn from A on BC in the triangle ABC, show that, h=(a sin B sin C)/(sin(B+C)) .

In Delta ABC,AB= AC and E is any point on the extended BC. The circumeircel of Delta ABC intersects AE at the point D. Prove that angle ACD= angle AEC .

I is the incentre of Delta ABC , Produced AI bisects BC at D. Prove that Delta ABC is isosceles.

On the outside of the equilateral triangle ABC and in the angular region angleABC , O is a point. OP, OQ and OR are the perpendiculars drawn from O to the sides. AB, BC and CA respectively. Prove that the height of the triangle = OP + OQ - OR.

In DeltaABC , AB = AC. The perpendiculars drawn from B and C to AC and AB respectively, intersect the sides AC and AB at the points E and F respectively. Prove that FE||BC.

Modhurima have drawn a semicircle with a diameter AB . A perpendicular is drawn on AB from any point C on AB which intersects the semicircle at the point D . Prove that CD is a mean proportion of AC and BC .