ABC is a cyclic equilaterla triangle. If P be any point on the are BC opposite to the point A, then prove that `AP=BP+CP`

The equilateral triangle ABC is inscribed in a circle. If P is any point on the ar BC, then prove that AB=PB+PC .

Delta ABC is an equilateral triangle . D is a point on the side BC such that BD = (1)/(3) BC . Prove that 7 AB^(2) = 9AD^(2)

If ABC is an isosceles triangle and D is a point on BC such that AD bot BC , then____

ABCD is a cyclic quadrilateral. The two sides AB and CD are produced to meet in the point P and other two sides AD and BC are produced to meet in the point R . The two circumcircle of DeltaBCPandDeltaCDR intersect at the point T . Prove that points P , T , R are collinear.

In an equilateral triangle ABC, D is a point on side BC such that BD = (1)/(3) BC. Prove that 9 AD^(2) = 7 AB^(2) .

If P is a point on the altitude AD of the triangle ABC such that angleCBP=B/3, then APis

If P(A//B)=1 then prove that, P(ABC)=P(BC) .

ABC is a right triangle right angled at B. Let D and E be any points on AB and BC respectively. Prove that AE^(2) + CD^(2) = AC^(2) + DE^(2) .

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