In the `DeltaOAB,M` is the mid-point of AB,C is a point on OM, such that 2OC=CM. X is a point on the side OB such that OX=2XB. The line XC is produced to meet OA in Y. then, `(OY)/(YA)` is equal to

C is the midpoint of the line segment bar(AB) and O is any point outside AB, show that vec(OA)+vec(OB)=2vec(OC) .

E is the mid point of side OB of triangle OAB . D is a point on AB such that AD : DB = 2 : 1 . If OD and AE intersect at P , then -

P( h, k) is the mid-point of a line segment between axes. Show that equation of the line is x/a + y/b = 2 .

O is the mind-point of AB in Delta ABC and OA=OB=OC , if a circle is drawn y taking AB as a diameter then the circle will pass through the point. C

In right triangle ABC, right angle is at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see figure). Show that : (i) DeltaAMC ~= DeltaBMD (ii) /_DBC is a right angle (iii) Delta DBC ~= DeltaACB (iv) CM = 1/2 AB .

Suppose A, B are two points on 2x-y+3=0 and P(1,2) is such that PA=PB. Then the mid point of AB is

Find the equation to the locus of mid-points of chords drawn through the point (a, 0) on the circle x^(2) + y^(2) = a^(2) .

P is a point on the line y+2x=1, and Qa n dR two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is

In the trapezium ABCD, AD || BC. X and Y are the mid-points of AB and DC. If XY = 10 cm, then find the sum of the length of its parallel sides.

If O is the origin and A(2, 3, 1), B(1, 1, -5) are two given points then show that the straight line OA is perpendicular to the straight line OB.