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)` `2RsinAsinBsinC` (d) `/R`

In acute angled triangle ABC,AD is the altitude.Circle drawn with AD as its diameter cuts AB and AC at P and Q, respectively. Length of PQ is equal to (phi)/(2R) (b) (abc)/(4R^(2))2R sin A sin B sin C(d)(del)/(R)

A B C D is a rhombus and P ,\ Q ,\ R ,\ S are the mid-points of A B ,\ B C ,\ C D ,\ D A respectively. Prove that P Q R S is a rectangle.

In a triangle A B C , let P a n d Q be points on A Ba n dA C respectively such that P Q || B C . Prove that the median A D bisects P Qdot

ABC is an equilateral triangle of side 4cm. If R,r and h are the circumradius,inradius, and altitude,respectively,then (R+h)/(h) is equal to 4(b)2(c)1(d)3

In A B C ,/_A=90^0a n dA D is an altitude. Complete the relation (B D)/(D A)=(A B)/(()) .

If ' O ' is the circum centre of the A B C and R_1,\ R_2,\ R_3 are the radii of the circumcircle of triangle O B C ,\ O C A\ a n d\ O A B respectively then a/(R_1)+b/(R_2)+c/(R_3) has the value equal to (a b c)/(2R^3) (b) (R^3)/(a b c) (c) (4)/(R^2) (d) (a b c)/(R^3)

ABCD is a cyclic quadrilateral. The bisectors of the angles A, B, C and D. cut the circle at P, Q, R and S respectively. What is anglePQR + angleRSP equal to ?

Let A B C D be a tetrahedron such that the edges A B ,A Ca n dA D are mutually perpendicular. Let the area of triangles A B C ,A C Da n dA D B be 3, 4 and 5sq. units, respectively. Then the area of triangle B C D is 5sqrt(2) b. 5 c. (sqrt(5))/2 d. 5/2

In a right angle triangle,if r=2,R=6 then area of the triangle is (A) 14 (B) 42 (C) 28 (D) 56

Let aandb represent the lengths of a right triangles legs.If d is the diameter of a circle inscribed into the triangle,and D is the diameter of a circle circumscribed on the triangle,the d+D equals.(a)a + b (b) 2(a+b)(c)(1)/(2)(a+b)( d) sqrt(a^(2)+b^(2))