P is an interior point of square ABCD. Prove that `PA+PB+PC+PD gt 2 AB`.

If P be any point in the plane of square ABCD, prove that PA^(2)+PC^(2)=PB^(2)+PD^(2)

In the given figure,ABCD is a square and P is a point inside it such that PB=PD. Prove that CPA is a straight line.

[" An equilateral triangle "ABC" is inscribed in a circle.P is any point on the minor are BC.Prove "],[" that "PA=PB+PC]

In the given figure, ABCD is a square and P is a point inside it such PB = Pd. Prove that CPA is a straight line.

In the given Fig. 5, from an external point P, a tangent PT and a secant PAB is drawn to a circle with centre 0. ON is perpendicular on the chord AB. Prove that PA.PB = PT^(2) ?.

There is a point P in a rectangle ABCD, such that PA = 4, PD = 5, PB = 8, find PC.

Let ABCD be a square and let P be point on segment CD such that DP : PC = 1 : 2. Let Q be a point on segment AP such that angleBQP = 90^@ . Then the ratio of the area of quadrilateral PQBC to the area of the square ABCD is

If P be a point in the interior of equilateral triangle ABC such that PA=3,PB=4 and PC=5 then find a.

In the given figure, ABCD is a parallelogram. Point P is at BC such that PB : PC = 1 : 2. The extended DP and extended AB meets at point Q. If the area of BPQ is 20 "unit"^(2) then find the area of DeltaDCP .