Home
Class 9
MATHS
Two congruent circles intersect each ot...

Two congruent circles intersect each other at points A and B. Through A any linesegment PAQ is drawn so that P, Q lie on the two circles. Prove that `B P\ =\ B Q`.

Text Solution

Verified by Experts

Let point `C` and `D` be the centres of the two congruent circles.
Let `AB` be the common chord.
`arc AEB=arc AFB` (arcs of congruent chords of congruent circles)
`/_APB=/_AQB` (angles subtended by congruent arcs)
...
Promotional Banner

Similar Questions

Explore conceptually related problems

Two congruent circles intersect each other at points A and B. Through A any line segment PAS is drawn so that P, Olie on the two circles. Prove that BP = BQ.

Two circles intersect each other at point P an Q. If PA and PB are two diameter then find angleAQB .

In figure, two circles intersect each other at points S and R. Their common tangent PQ touches the circle at points P,Q. Prove that, /_PRQ+/_PSQ=180^(@) .

In the figure, two circles intersect each other at points A and B. AP and AQ are the diameters of these circels. Prove that PBQ is a straight line.

Two circles intersect each other at P and Q. PA and PB are two diameters. Then angleAQB is

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

The congruent circles with centres Oand O' intersect at two points A and B. Then, angleAOB=angleAO'B .

Two circles intersect at two points A and B . AD and AC are diameters to the two circles .Prove that B lies on the line segment DC.

Two circles intersect each other at point P and Q. Secants drawn through p and Q intersect the circles at points A,B and D,C Prove that : /_ ADC + /_ BCD = 180^(@)

Two circles intersect at two points B and C . Through B,two line segments ABD and PBQ are drawn to intersect the circles at A,D and P, Q respectively (see Fig.10.40). Prove that /_ACP=/_QCD