Two chords AB and AC of the larger of two concentrci circles touch the other circle at points P and Q respectively. Prove that `PQ = 1/2BC`.

PQ is a chord of the circle with centre at O. Draw two tangents at P and Q respectively .

Three points P,Q ,R lie on a circle. The two perpendiculars PQ and PR and the point P intersect the circle at the points S and T respectively. Prove that RQ=ST

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 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

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.

In the adjoining figure, two tangents drawn from external point C to a circle with centre O touches the circel at the point P and Q respectively. A tangent drawn at another point R of the circle intersects CP and CQ at the points A and B respectively. If CP = 7 cm and BC =11 cm, then determine the length of BR.

The internal and external bisectors of the vertical angle of a triangle intersect the circumcircle of the triangle at the points P and Q. Prove that PQ is a diameter of the circle.

Two circles touch each other externally at point A and PQ is a direct common tangent which touches the circles at P and Q respectively. Then anglePAQ =

Two circles intersect each other at the points G and H . A straight line is drawn through the point G which intersect two circles at the points P and Q and the straight line through the point H parallel to PQ intersects the two circles at the points R and S . Prove that PQ=RS .