A circle passes through the points `A(1,0)` and `B(5,0),` and touches the y-axis at `C(0,h)dot`. If `/_A C B` is maximum, then
(a)`h=3sqrt(5)`
(b) `h=2sqrt(5)`
(c)`h=sqrt(5)`
(d) `h=2sqrt(10)`

(a) sqrt(175) (b) 2sqrt(112) (c) sqrt(125) (d) 5sqrt(119)

Tangents are drawn to x^2+y^2=16 from the point P(0, h)dot These tangents meet the x- axis at Aa n dB . If the area of triangle P A B is minimum, then h=12sqrt(2) (b) h=6sqrt(2) h=8sqrt(2) (d) h=4sqrt(2)

The equation of the lines passing through the point (1,0) and at a distance (sqrt(3))/2 from the origin is (a) sqrt(3)x+y-sqrt(3) =0 (b) x+sqrt(3)y-sqrt(3)=0 (c) sqrt(3)x-y-sqrt(3)=0 (d) x-sqrt(3)y-sqrt(3)=0

The radius of the tangent circle that can be drawn to pass through the point (0, 7) and (0, 6) and touching the x-axis is (a) 5/2 (b) 13/2 (c) 7/2 (d) 19/2

y^(2)=4xandy^(2)=-8(x-a) intersect at points A and C. Points O (0,0) , A,B (a,0) , and C are concyclic. The area of cyclic quadrilateral OABC is (a) 24sqrt(3) (b) 48sqrt(2) (c) 12sqrt(6) (d) 18sqrt(5)

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

A B C D is a square of unit area. A circle is tangent to two sides of A B C D and passes through exactly one of its vertices. The radius of the circle is (a) 2-sqrt(2) (b) sqrt(2)-1 (c) sqrt(2)-1/2 (d) 1/(sqrt(2))

In a A B C , if tanA:tanB :tanC=3:4:5, then the value of sinA sinB sinC is equal to (a) 2/(sqrt(5)) (b) (2sqrt(5))/7 (2sqrt(5))/9 (d) 2/(3sqrt(5))

In A B C , the coordinates of the vertex A are (4,-1) , and lines x-y-1=0 and 2x-y=3 are the internal bisectors of angles Ba n dC .Then, the radius of the encircle of triangle A B C is (a) 4/(sqrt(5)) (b) 3/(sqrt(5)) (c) 6/(sqrt(5)) (d) 7/(sqrt(5))

If A(1,p^2),B(0,1) and C(p ,0) are the coordinates of three points, then the value of p for which the area of triangle A B C is the minimum is (a) 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) 1/(sqrt(2)) (d) none of these