If the equal sides `AB and AC` each of whose length is `2a` of a righ aisosceles triangle `ABC` be produced to P and so that `BP. CQ=AB,` the line `PQ` always passes through the fixed point

If the equal sides AB and AC each of whose length is a of a righ aisosceles triangle ABC be produced to P and so that BP. CQ=AB^2, the line PQ always passes through the fixed point

If the equal sides AB and AC (each equal to 5 units) of a right-angled isosceles triangle ABC are produced to P and Q such that BP cdot CQ = AB^(2) , then the line PQ always passes through the fixed point (where A is the origin and AB, AC lie along the positive x and positive y - axis respectively)

A line segment AB is 8 cm in length. AB is produced to P such that BP^(2)=AB.AP, find the length of BP.

D is a point in side BC of triangle ABC. If AD gt AC , show that AB gt AC .

If AB, AC are equal sides of an isosceles triangle, prove that "tan"(A)/(2)=cotB .

The sides AB and AC of a triangle ABC are produced, and the bisectors of the external angles at B and C meet at P. Prove that if AB gt AC , then PC gt PB .

In a triangle ABC, sides AB and AC are of equal length. If angleB=35^(@) , find the measure of angleA and angleC .

Describe the locus of a point P, so that : AB^(2)=AP^(2)+BP^(2) , where A and B are two fixed points.

The sides AB and AC are equal of an isosceles triangle ABC. D E and F are the mid-points of sides BC, CA and AB respectively. Prove that: (i) Line segment AD is perpedicular to line segment EF. (ii) Line segment AD bisects the line segment EF.

The sides AB and BC and the median AD of triangle ABC are equal to the sides PQ and QR and the median PM of triangle PQR respectively. Prove that the triangles ABC and PQR are congruent.