Line segments `A C` and `B D` are diameters of the circle of radius 1. If `/_B D C=60^0` , the length of line segment `A B` is_________

Line segments A C and B D are diameters of the circle of radius one. If /_B D C=60^0 , the length of line segment A B is_________

A B\ a n d\ C D are diameters of a circle with centre Odot If /_O B D=50^0, find /_A O C

Let C be the mid-point of an arc A B of a circle such that m\ hat A B=183^0dot If the region bounded by the arc A C B and line segment A B is denoted by S , then the centre O of the circle lies (a) in the interior of S (b) in the exterior of S on the segment A B (d) on A B and bisects A B

Line segments AB and CD intersect at O such that A C||D B . If /_C A B=35^0 and /_C D B=55^0 find the /_B O Ddot

In Figure, A P\ a n d\ B Q are perpendiculars to the line segment A B\ a n d\ A P=B Q . Prove that O is the mid-point of line segment A B\ a n d\ P Q

Let the orthocentre and centroid of a triangle be A(-3,5) and B(3,3) respectively. If C is the circumcentre of the triangle then the radius of the circle having line segment AC as diameter, is

Let C be a circle with centre P_(0) and AB be a diameter of C . suppose P_(1) is the midpoint of line segment P_(0) B, P_(2) the midpoint of line segment P_(1) B and so on Let C_(1),C_(2) ,C_(3) be circles with diameters P_(0)P_(1), P_(1)P_(2),P_(2)P_(3) ,... respectively Suppose the circles C_(1),C_(2),C_(2), ... are all shaded The ratio of the area of the unshaded portion of C to that of the original circle is

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 Figure). Prove that /_A C P=/_Q C D .

In the given figure A B is the diameter of the circle, centred at Odot If /_C O A=60^0,A B=2r ,A C=d , and C D=l , then l is equal to (a) dsqrt(3) (b) d//sqrt(3) (c) 3d (d) sqrt(3) d /2

Two segments A C and B D bisect each other at O . Prove that A B C D is a parallelogram.