An acute triangle PQR is inscribed in the circle `x^2+y^2= 25`. If Q and R have coordinates (3, 4) and (-4, 3) respectively, then find `/_QPR`.

A right angled isosceles triangle is inscribed in the circle x^2 + y^2 -4x - 2y - 4 = 0 then length of its side is

The line x+y=p meets the x- and y-axes at Aa n dB , respectively. A triangle A P Q is inscribed in triangle O A B ,O being the origin, with right angle at QdotP and Q lie, respectively, on O Ba n dA B . If the area of triangle A P Q is 3/8t h of the are of triangle O A B , the (A Q)/(B Q) is equal to (a) 2 (b) 2/3 (c) 1/3 (d) 3

Let ABC be an acute- angled triangle and AD, BE, and CF be its medians, where E and F are at (3,4) and (1,2) respectively. The centroid of DeltaABC , G(3,2) . The coordinates of D are

If the ordered pairs (x^2-3y,y^2+4y) and (-2,5) are equal , then find x and y .

A square is inscribed in the circle x^2+y^2-2x+4y+3=0 . Its sides are parallel to the coordinate axes. One vertex of the square is (a) (1+sqrt(2),-2) (b) (1-sqrt(2),-2) (c) (1,-2+sqrt(2)) (d) none of these

The acute angle between the line 3x-4y=5 and the circle x^2+y^2-4x+2y-4=0 is theta . Then 9costheta=

If the straight line x - 2y + 1 = 0 intersects the circle x^2 + y^2 = 25 at points P and Q, then find the coordinates of the point of intersection of the tangents drawn at P and Q to the circle x^2 + y^2 = 25 .

An equilateral triangle is inscribed in an ellipse whose equation is x^2+4y^2=4 If one vertex of the triangle is (0,1) then the length of each side is

In acute angled triangle A B C ,A D is the altitude. Circle drawn with A D as its diameter cuts A Ba n dA Ca tPa n dQ , respectively. Length of P Q is equal to /(2R) (b) (a b c)/(4R^2) (c) 2RsinAsinBsinC (d) delta/R

If the ordered pairs (x^(2) - 3x, y^(2) + 4y ) and (-2,5) are equal , then find x and y .