In ` A B C ,C=60^0a n dB=45^0dot` Line joining vertex A of triangle and its circumcenter `(O)` meets the side `B CinD` Find the ratio `B D : D C` Find the ratio `A O : O D`

Line joining vertex A of triangle ABC and orthocenter (H) meets the side BC in D. Then prove that (a) BD : DC = tan C : tan B (b) AH : HD = (tan B + tan C) : tan A

In triangle ABC ,the line joining the circumcenter and incenter is parallel to side AC, then cos A+cos C is equal to -1 (b) 1 (c) -2(d)2

ABC is a triangle in which /_A=72^(0), the internal bisectors of angles B and C meet in O. Find the magnitude of /_BOC.

If O is a point in space, A B C is a triangle and D , E , F are the mid-points of the sides B C ,C A and A B respectively of the triangle, prove that vec O A + vec O B+ vec O C= vec O D+ vec O E+ vec O Fdot

If in a ABC,/_A=45^(0),/_B=60^(0), and /_C=75^(@) ,find the ratio of its sides.

In A B C , /_B=60^0,/_C=40^0, A L_|_B C a n d A D bisects /_A such that L and D lie on side B Cdot Find /_L A Ddot

Draw a triangle ABC with BC=7cm, /_B=45^0a n d/_C=60^0dot Then construct another triangle, whose sides are 3/5 times the corresponding sides of triangle A B Cdot

In Figure, A B C D is a parallelogram and /_D A B=60^0dot If the bisectors A P\ a n d\ B P of angles A\ a n d\ B respectively, meet at P on C D , prove that P is the mid-point of C D

The base of the pyramid A O B C is an equilateral triangle O B C with each side equal to 4sqrt(2),O is the origin of reference, A O is perpendicualar to the plane of O B C and | vec A O|=2. Then find the cosine of the angle between the skew straight lines, one passing though A and the midpoint of O Ba n d the other passing through O and the mid point of B Cdot

In a parallelogram A B C D diagonals A C\ a n d\ B D intersect at O\ a n d\ A C=6. 8\ c m\ a n d\ B D=5. 6 c m . Find the measures of O C\ a n d\ O D .