The two chords `PQ` and `RS` of a circle intersects each other at the point `X` within the circle. By joining `P,S` and `R,Q` prove that `DeltaPXS` and `DeltaRSQ` are similar. From this also prove that `PX: XQ=RX : XS`.

Two chords AB and CD of a circle intersect at a internal point P of the circle. Prove that APxxBP=CPxxDP .

Two circles intersect each other at P externally. The straight QR touches the circle at two points Q and R. Prove that /_QPR = 1 right angle.

DeltaABC is inscribed in a circle, AD is a diameter of the circle and AE is perpendicular on the side BC , which intersects the side BC at the point E . Prove that DeltaAEB and DeltaACD are similar. From this also prove that ABxxAC=AExxAD .

Two chords AB and CD of the circle with centre at O intersect each other at an internal point P of the centre. Prove that angle AOD+ angle BOC=2 angle BPC

Two chords AB and CD of a circle with centre O intersect each other at the point P. If ∠AOD =20° and ∠BOC = 30°, then ∠BPC is equal to?

If two chords AB and CD of a circle with centre O, when produce intersect each other at the point P, then prove angleAOC-angleBOD = 2angleBPC .

Two chord PQ and PR of the circle are perpendicular to each other. If the radius of the circle be r and then find the length of the chord QR.

If two chords AB and CD of a circle with centre, O, when producd intersect each other at the point P, prove that angle AOC- angle BOD=2 angle BPC .

Two tangents drawn at the point A and B on a circle intersect each other at the point P. If angle APB=60^(@), then anglePAB=

Two chords AC and BD of a circle intersect each other at the point O. If two tangents drawn at the points A and B intersect each other at the point P and two tangents drawn at the points C and D intersect at the point Q, prove that angle P+ angle Q =2 angle BOC. [GP-X]