The chord of contact of tangents from a point `P` to a circle passes through `Qdot` If `l_1a n dl_2` are the length of the tangents from `Pa n dQ` to the circle, then `P Q` is equal to `(l_1+l_2)/2` (b) `(l_1-l_2)/2` `sqrt(l1 2+l2 2)` (d) `2sqrt(l1 2+l2 2)`

The lengths of the tangents from the points A and B to a circle are l_(1) and l_(2) respectively. If points are conjugate with respect to the circle, then AB^(2)=

If L_1&L_2 are the lengths of the segments of any focal chord of the parabola y^2=x , then (a) 1/(L_1)+1/(L_2)=2 (b) 1/(L_1)+1/(L_2)=1/2 (c) 1/(L_1)+1/(L_2)=4 (d) 1/(L_1)+1/(L_2)=1/4

l and m are the lengths of the tangents from the origin and the point (9, -1) to the circle x^(2) + y^(2) + 18x - 2y + 32 = 0 . The value of 17(l^(2) + m^(2)) is equal to ________ .

If l, l_(1), l_(2) and l _(3) be respectively the radii of the in-circle and the three escribed circles of a Delta ABC, then find l_(1)l_(2) l_(3)-l(l_(1)l_(2) +l_(2) l_(3)+l_(1) l_(3)).

If l_(1), l_(2), l_(3) are respectively the perpendicular from the vertices of a triangle on the opposite side, then show that l_(1)l_(2) l_(3) =(a^(2)b ^(2) c^(2))/(8R^(3)).

theta_1 and theta_2 are the inclination of lines L_1 and L_2 with the x-axis. If L_1 and L_2 pass through P(x_1,y_1) , then the equation of one of the angle bisector of these lines is

If the lines L_1a n dL_2 are tangents to 4x^2-4x-24 y+49=0 and are normals for x^2+y^2=72 , then find the slopes of L_1 and L_2dot

If a line, y = mx + c is a tangent to the circle, (x-1)^2 + y^2 =1 and it is perpendicular to a line L_1 , where L_1 is the tangent to the circle x^2 + y^2 = 8 at the point (2, 2), then :

A lamp of negligible height is placed on the ground l_1 away from a wall. A man l_2m tall is walking at a speed of (l_1)/(10)m//s from the lamp to the nearest point on the wall. When he is midway between the lamp and the wall, the rate of change in the length of this shadow on the wall is (a) -(5l_2)/2m//s (b) -(2l_2)/5m//s (c) -(l_2)/2m//s (d) -(l_2)/5m//s

If P is any arbitrary point on the circumcircle of the equilateral triangle of side length l units, then | vec P A|^2+| vec P B|^2+| vec P C|^2 is always equal to 2l^2 b. 2sqrt(3)l^2 c. l^2 d. 3l^2