P is any point in the angle ABC such that the perpendiculars drawn from P on AB and BC are equal. Prove that BP bisects angle ABC.

P is any point in the angle ABC such that the perpendicular drawn from P on AB and BC are equal. Prove that BP bisects angle ABC.

If AP bisects angle BAC and M is any point on AP, prove that the perpendiculars drawn from M to AB and AC are equal.

ABC is a triangle and D is the mid-point of BC .The perpendiculars from D to AB and AC are equal.Prove that the triangle is isosceles.

The vertices of a triangle ABC are the points (0, b), (-a, 0), (a, 0) . Find the locus of a point P which moves inside the triangle such that the product of perpendiculars from P to AB and AC is equal to the square of the perpendicular to BC .

The vertices of a triangle ABC are the points (0, b), (-a, 0), (a, 0) . Find the locus of a point P which moves inside the triangle such that the product of perpendiculars from P to AB and AC is equal to the square of the perpendicular to BC .

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 .

ABC s a triangle and D is mid-point of BC. Perpendiculars froms D to AB and AC are equal. Prove that triangle is isosceles.

A triangle ABC has angle B = angle C . Prove that : (i) the perpendiculars from the mid-point of BC to AB and AC are equal. (ii) the perpendicular from B and C to the opposite sides are equal.

BD is the disector of angle ABC. From a point P in BD, perpendiculars PE and PF are drawn to AB and BC respectively, prove that : (i) Triangle BEP is conguent to triangle BFP (ii) PE=PF.