In the adjoining figure, the vertices of square DEFG are on the sides of `DeltaABC`. If `angleA = 90^@`, then prove that `DE^2 = BD xx EC`.

In the adjoining figure, AB~=CD . Prove that arc AC ~=arc BD

In the adjoining figure, the circle is the incircle of isosceles DeltaABC , where seg AB = seg AC. Prove that M bisects BC.

In the adjoining figure, in DeltaABC , point D is on side BC such that, angleBAC = angleADC . Prove that, CA^2 = CB xx CD .

In the adjoining figure, bisector of angleBAC intersects BC at point D. Prove that AB gt BD .

In the adjoining figure, point S is on side QR of DeltaPQR . Prove that PQ + QR + RP gt 2PS

In the adjoining figure, seg AB is a diameter of a circle with centre O. the bisector of angleACB intersects the circle at point D. Prove that ,seg ADcongseg BD .

In the adjoining figure, seg AD bot side BC, seg BE bot side AC, seg CF bot side AB. Point O is the orthocentre. Prove that , point O is the incentre of DeltaDEF .

In the adjoining figure, seg YZ and seg XT are altitudes of triangle WXY which intersect each other at point P. Prove that square WZPT is a cyclic quadrilateral.

In the adjoining figure, O is the centre and seg AB is a diameter. At point C on the circle, the tangent CD is drawn. Line BD is tangent at B. Prove that seg OD||seg AC

In the adjoining figure, O is the centre of the circle. Seg AB, seg AC are tangent segments. Radius of the circle is r and l(AB) = r. Prove that , square ABOC is a square.