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_________

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 CD=l

Let A_0A_1A_2A_3A_4A_5 be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments A_0A_1 , A_0A_2 and A_0A_4 is

From the figure, answer the following : (b) Line segment OQ is the ______ of the circle.

In a triangle A B C , the bisectors of angles Ba n dC lies along the lines x=y a n d y=0. If A is (1,2) , then the equation of line B C is

AB is a line segment of length 48 cm and C is its mid-point. If three semicircles are drawn at AB, AC and CB using as diameters, then radius of the circle inscribed in the space enclosed by three semicircles is

Let a and b represent the lengths of a right triangles legs. If d is the diameter of a circle inscribed into the triangle, and D is the diameter of a circle circumscribed on the triangle, the d+D equals. (a) a+b (b) 2(a+b) (c) 1/2(a+b) (d) sqrt(a^2+b^2)

From the figure, answer the following : (c) Line segment PQ is ______ of circle.

Let AB be a line segment of length 4 unit with the point A on the line y=2x and B on the line y=x. Then locus of middle point of all such line segment is

Consider square A B C D of side length 1. Let P be the set of all segments of length 1 with endpoints on the adjacent sides of square A B C D . The midpoints of segments in P enclose a region with area Adot The value of A is (a) pi/4 (b) 1-pi/4 (c) 4-pi/4 (d) none of these

Let the base A B of a triangle A B C be fixed and the vertex C lies on a fixed circle of radius rdot Lines through Aa n dB are drawn to intersect C Ba n dC A , respectively, at Ea n dF such that C E: E B=1:2a n dC F : F A=1:2 . If the point of intersection P of these lines lies on the median through A B for all positions of A B , then the locus of P is (a) a circle of radius r/2 (b) a circle of radius 2r (c) a parabola of latus rectum 4r (d) a rectangular hyperbola