AB is a diameter of a circle with centre O and AC is a chord . The straight line through O parallel to AC meets the arc BC at D. Prove that, BD= CD.

AB is a diameter and AC is a chord of the circle with centre at Q. the radius parallel to AC intersect the circle at D. Prove that D is the mid-point of the are BC.

Two circle intersect each other at A and B and a straight line parallel to AB intersects the circles at C,D,E,F. Prove that CD = EF.

AB is a diameter of a circle. BP is a tangent to the circle at B . A straight line passing through A intersects BP at C and the circle at D . Prove that BC^(2)=ACxxCD .

AB is a diameter of a circle with centre at O. If chord CD bot AB and angleCAD = 80^@ , then angleADC =

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.

AC is a diamter of a circle with centre O, If triangleABC is cyclic and OP bot AB , then prove that OP:BC = 1:2.

AD is a median of triangleABC . A straight line parallel to BC intersect AB and AC at P and Q respectively. Prove that AD bisects PQ.

AB is a diameter of a circle with centre at O. Chord PQ intersects AB in such a way that angleAOP = 130^@ . The value of anglePQB is

AB is a diameter of a circle. CD is a chord parallel to AB and 2CD = AB . The tangent at B meets the line AC produced at E then AE is equal to -

If the vector product of a constant vector vec O A with a variable vector vec O B in a fixed plane O A B be a constant vector, then the locus of B is a. a straight line perpendicular to vec O A b. a circle with centre O and radius equal to | vec O A| c. a straight line parallel to vec O A d. none of these