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.

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 .

An isosceles triangle ABC is right angled at B.D is a point inside the triangle ABC. P and Q are the feet of the perpendiculars drawn from D on the sides AB and AC respectively of Delta ABC . If AP = a cm, AQ = b cm and angle BAD= 15^(@), sin 75^(@)=

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.

From a point O inside a triangle ABC , perpendiculars OD,OE and Of are drawn to rthe sides BC,CA and AB, respecrtively. Prove that the perpendiculars from A,B, and C to the sides EF, FD and DE are concurrent.

ABC is a triangle right angled at C. Let p be the length of the perpendicular drawn from C on AB. If BC = 6 cm and CA = 8 cm, then what is the value of p ?

ABC is a triangle right angled at Aand a perpendicular AD is drawn on the hypotenuse BC. What is BC.AD equal to ?

let ABC be a triangle with AB=AC. If D is the mid-point of BC, E the foot of the perpendicular drawn from D to AC,F is the mid-point of DE.Prove that AF is perpendicular to BE.