Seg AB is a diameter of a circle with centre P(1,2). If A(-4,2), then find the co-ordinates of point B.

In the adjoining figure, seg AB is a diameter of a circle with centre O. the bisector of angleACB intersects the circle at point D. Prove that ,seg ADcongseg BD .

In the adjoining figure, seg AB is a diameter of a circle with centre C. Line PQ is a tangent, which touches the circle at point T. Seg AP bot line PQ and seg BQ bot line PQ. Prove that seg CP cong seg CQ.

In the adjoining figure, seg AB is a diameter of a circle with centre O. Bisector of inscribed /_ACB intersects circle at point D. prove: seg AD~=seg BD

In the above figure, seg AB is a diameter of a circle with centre P.C is any point on the circle. Seg CE _|_ seg AB. Prove that CE is the geometric mean of AE and EB. Write the proof with the help of following steps: (a) Draw ray CE. It intersects the circle at D. (b) Show that CE = ED. Write the result using theorem of intersection of chords insides a circle. (d) Using CE = ED, complete the proof.

If A (3,5) , B (7,9) and Q divides seg AB in the ratio 2:3 , then find the co-ordinates of points Q .

Seg AB is parallel to Y-axis and co-ordinates of point A are (1,3), then co-ordinates of point B can be……….a) (3,1) b) (5,3) c) (3,0) d) (1,-3)

If A-P-Q-B, point P and Q trisects seg AB and A(3,1) , Q(-1,3), then find coordinates of points B and P.

In the adjoining figure, seg EF is the diameter of the circle with centre H. Line DF is tangent at point F. If r is the radius of the circle, then prove that DE xxGE=4r^2 .

In the adjoining figure, seg AB is a chord of a circle with centre P. If PA = 8 cm and distance of chord AB from the centre P is 4 cm, find the area of the shaded portion. (pi = 3.14. sqrt3 = 1.73)

In the adjoining figure, seg RS is the diameter of the circle with centre 'O'. Point T is in the exterior of the circle. Prove that /_RTS is an acute angle.