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`.

In right triangle ABC, right angled at C, M is the midpoint 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 the given figure). Show that: (i) triangle AMC = triangleBMD (ii) angle DBC is a right angle (iii) triangleDBC = triangleACB (iv) CM=1/2 AB

In a right angle triangle ABC, right angle is at C, BC+CA = 23 cm and BC-CA = 7cm ,then find sin A tan B

In triangle ABC, right angled at B, if tanA=1/(sqrt3) . Find the value of cos A cos C - sin A sin C

D is a point on side BC of triangle ABC such that AD = AC (see the given figure). Show that AB gt AD.

In triangle ABC, right angled at B, if tanA=1/(sqrt3) . Find the value of sin A cos C + cos A sin C

In a right angle triangle ABC, right angle is at B ,If tan A=sqrt(3) , then find the value of (i) sin A cos C+ cos A sin C " "(ii) cos A cos C -sin A sin C

ABC is a triangle right angled at C. A line through the midpoint M of hypotenuse AB and Parallel to BC intersects AC at D. Show that (i) D is the midpoint of AC (ii) MD_|_AC (iii) CM=MA=(1)/(2)AB.

triangle ABC is an isosceles tr ia n g le in w h ich AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that angle BCD is a right angle.

In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD (see the given figure). Show that AD = AE.

In the triangle OAB , M is the midpoint of AB, C is a point on OM, such that 2 OC = 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)=