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

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 intersect at the point P, which is inside the circle and O is the centre of the circle. If angleAOC = 55^@ , and angleBOD =45^@ , then angleAPC =

Two chords AB and CD of a circle with centre O intersect each other at the point P. prove that AOD+ angle BOC = 2 angle PBC . If angle BOC are supplementary to each other, then prove that the two chords are perpendicular to each other.

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 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]

Two chords AB and CD of a cricle with centre O intersect at P. Prove that angleAOD+angleBOC= 2 angleBPC .

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 .

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 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?

Chords AB and CD of a circle intersect inside the circle at point E. If AE = 5.6, EB = 10, CE = 8, find ED.