O হল একটি DeltaABC এর বাইরের যেকোনো বিন্দু। প্রমাণ কর যে 2(OA + OB + OC) gt (AB + BC + CA)। | সিএল...

In DeltaABC, D is any point on side BC. Prove that AB+BC+CA gt 2AD

If O is point in the exterior of triangleABC ,show that 2(OA+OB+OC)gt(AB+BC+CA)

Let O be an interior point of DeltaABC such that bar(OA)+2bar(OB) + 3bar(OC) = 0. Then the ratio of a DeltaABC to area of DeltaAOC is

O is a point in the interior of Delta ABC, OD bot BC, OE bot AC and OF bot AB , as shown in the figure, Prove that : (i) OA^(2)+OB^(2)+OC^(2)-OD^(2)-OE^(2)-OF^(2)=AF^(2)+BD^(2)+CE^(2) (ii) AF^(2)+BD^(2)+CE^(2)=AD^(2)+BF^(2)+CD^(2)

Let d(P, OA) le min {d (P, AB), d(P, BC), d (P, OC)} where d denotes the distance from the point to the corresponding line and S be the region consisting of all those points P inside the rectangle OABC such that O = (0, 0), A = (3, 0), B = (3, 2) and C = (0, 2), which satisfy the above relation, then area of the region S is

If G be the centroid of the DeltaABC and O be any other point in theplane of the triangle ABC , then prove that: OA^2 +OB^2 +OC^2=GA^2 +GB^2 +GB^2 + GC^2 + 3GO^2

In the given fig., AB || DC and diagonals AC and BD intersects at O. If OA =3x-1 and OB =2x + 1, OC = 5x-3 and OD =6x-5, find the value of x.

ABC is a given triangle. AD, BE and CF are altitudes of DeltaABC . Assertion (A) : (AB^(2)+BC^(2)+CA^(2)) gt (AD^(2)+BE^(2)+CF^(2)) Reason (R) : (AE^(2)-AF^(2))+(BF^(2)-BD^(2))+(CD^(2)-CE^(2))=0

Consider a triangle OAB on the xy- plane in which O is taken as origin of reference and position vector of A and B are vec aandvec b respectively. A line AC parallel to OB is drawn a from A. D is the mid point of OA. Now a line DC meets AB at M. Area of DeltaABC is 2 times the area of DeltaOAB On the basis of above information, answer the following questions 1. Position vector of point C is 2. Position vector of point M is