A straight line intersects one of the two concentric circles at the points A and B and other at the points C and D. Prove that AC = BD.

Ankita drew two circles which intersect each other at the points P and Q. Through the point P two straight lines are draw so that they intersect one of the circle at the points. A and B and the ohte circle at the points C and D respectively. Prove that angle AQC= angle BQD .

Two circles intersect each other at the points P and Q. Two straight lines through P and Q intersect on circle at the points A and C and the other circle at B and D . Prove that AC||BD.

The centre of two concetric circles is O. A straight line intersects one of the circles at A and B and the other cirlce at C and D respectively . If AC = 5 cm , then the length of BD is [GP-X]

AB is a diameter of a circle with centre O . A line drawn through the point A intersects the circle at the point C and the tangent through B at the point D . Prove that (a) BD^(2)=AD.DC . (b) The area of the rectangle of formed by AC and AD for any straight line is always equal.

Like the adjoining figure, draw two circles with centres C and D which intersect each other at the points A and B . Draw a straight line through A which intersects the circle C at the point P and the circle with centre D at the point Q. Prove that (i) angle PBQ= angle CAD (ii) angle BPC= angle BQD .

Debanjan drew a line segment PQ of which mid-point is R and two circles are drawn with PR adn PQ as diameter . Deberatee drew a straight line through the point which interects the first circle at the point S and the second circle at the point T. Prove that PS=ST

The centre of two circle are P and Q they intersect at the points A and B. The straight line parallel to the line segment PQ through the point A intersects the two circles at the point C and D Prove that CD = 2PQ

Two parallel straight lines intersect three concurrent straight lines at the points A , B , C and X,Y,Z respectively. Prove that AB : BC=XY : YZ .

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]