If a circle of radius `r` is touching the lines `x^2-4x y+y^2=0` in the first quadrant at points `Aa n dB` , then the area of triangle `O A B(O` being the origin) is (a)`3sqrt(3)(r^2)/4` (b) `(sqrt(3)r^2)/4` (c)`(3r^2)/4` (d) `r^2`

If a circle of radius r is touching the lines x^(2)-4xy+y^(2)=0 in the first quadrant at points AandB, then the area of triangle OAB(O being the origin) is (a)3sqrt(3)(r^(2))/(4) (b) (sqrt(3)r^(2))/(4)( c) (3r^(2))/(4) (d) r^(2)

If the radius of the circle passing through the origin and touching the line x+y=2 at (1, 1) is r units, then the value of 3sqrt2r is

If the radisu of the circle passing through the origin and touching the line x+y=2 at (1, 1) is r units, then the value of 3sqrt2r is

If a line y=3x+1 cuts the parabola x^2-4x-4y+20=0 at Aa n dB , then the tangent of the angle subtended by line segment A B at the origin is (8sqrt(3))/(205) (b) (8sqrt(3))/(209) (8sqrt(3))/(215) (d) none of these

The tangent at the point (alpha, beta) to the circle x^2 + y^2 = r^2 cuts the axes of coordinates in A and B . Prove that the area of the triangle OAB is a/2 r^4/|alphabeta|, O being the origin.

The tangent at the point (alpha, beta) to the circle x^2 + y^2 = r^2 cuts the axes of coordinates in A and B . Prove that the area of the triangle OAB is a/2 r^4/|alphabeta|, O being the origin.

The largest area of the trapezium inscribed in a semi-circle or radius R , if the lower base is on the diameter, is (a) (3sqrt(3))/4R^2 (b) (sqrt(3))/2R^2 (c) (3sqrt(3))/8R^2 (d) R^2

The largest area of the trapezium inscribed in a semi-circle or radius R , if the lower base is on the diameter, is (a) (3sqrt(3))/4R^2 (b) (sqrt(3))/2R^2 (3sqrt(3))/8R^2 (d) R^2

The largest area of the trapezium inscribed in a semi-circle or radius R , if the lower base is on the diameter, is (a) (3sqrt(3))/4R^2 (b) (sqrt(3))/2R^2 (3sqrt(3))/8R^2 (d) R^2

If tangents O Q and O R are dawn to variable circles having radius r and the center lying on the rectangular hyperbola x y=1 , then the locus of the circumcenter of triangle O Q R is (O being the origin). (a) x y=4 (b) x y=1/4 x y=1 (d) none of these