Let ABC be a triangle with `/_A=45^0dot` Let P be a point on side BC with PB=3 and PC=5. If O is circumcenter of triangle ABC, then length OP is `sqrt(18)` (b) `sqrt(17)` (c) `sqrt(19)` (d) `sqrt(15)`

Let A B C be a triangle with /_B=90^0 . Let AD be the bisector of /_A with D on BC. Suppose AC=6cm and the area of the triangle ADC is 10c m^2dot Find the length of BD.

In a triangle, the lengths of the two larger sides are 10 and 9, respectively. If the angles are in A.P., then the length of the third side can be (a) 5-sqrt(6) (b) 3sqrt(3) (c) 5 (d) 5+sqrt(6)

The vector vec(AB)=3hati+4hatk and vec(AC)=5hati-2hatj+4hatk are sides of a triangle ABC. The length of the median through A is (A) sqrt(18) (B) sqrt(72) (C) sqrt(33) (D) sqrt(288)

One angle of an isosceles triangle is 120^0 and the radius of its incircle is sqrt(3)dot Then the area of the triangle in sq. units is (a) 7+12sqrt(3) (b) 12-7sqrt(3) (c) 12+7sqrt(3) (d) 4pi

Prove that in triangle ABC, sin A+sin B+sin Cle(3sqrt(3))/(2)

In triangle A B C ,/_A=60^0,/_B=40^0,a n d/_C=80^0dot If P is the center of the circumcircle of triangle A B C with radius unity, then the radius of the circumcircle of triangle B P C is (a)1 (b) sqrt(3) (c) 2 (d) sqrt(3) 2

Consider a branch of the hypebola x^2-2y^2-2sqrt2x-4sqrt2y-6=0 with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is (A) 1-sqrt(2/3) (B) sqrt(3/2) -1 (C) 1+sqrt(2/3) (D) sqrt(3/2)+1

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 1/(sqrt(3)) (b) -1/(sqrt(3)) 1/(sqrt(2)) (d) none of these

A right triangle has perimeter of length 7 and hypotenuse of length 3. If theta is the larger non-right angle in the triangle, then the value of costhetae q u a ldot (sqrt(6)-sqrt(2))/4 (b) (4+sqrt(2))/6 (4-sqrt(2))/3 (d) (4-sqrt(2))/6