ICSE − Q & A

Please help!!! Urgent need...
Constructions: construct a triangle ABC in which AB=7cm, angle A=60° and altitude CD=3cm. Construct a circumcircle to the triangle.

Please help!!! ICSE specimen paper2016 section B question 7(c).

Please help!!
Banking: ICSE specimen paper 2016 question 7 (c) please help!!!

The bisector of angle BAC of triangle ABC meets the opposite side at D. A line, through vertex C of the triangle and parallel to DA, meets BA produced at E. 
Prove that 1)AE=AC 2)BD*AC=DC*AB
Please solve 2).
Ad can you tell which triangles to take for proving their similarity ?

i need a full written solution for page no. 304(problem no. 39)
concise book

Two vessels contain a mixture of two liquids A and B
in the ratio 9:4 and 5:3.In which ratio must the liquids
must be taken from each vessel to give a mixture of liquid A and liquid B in the ratio of 2:1?

On a graph paper plot the triangle ABC whose vertices are A() ,B() and C(). on the same graph , draw the image of the triangle ABC under reflection in the line y= 3 . Mark any two points which are invariant under reflection and also write their coordinates.. Kindly tell me which are the invariant points here and why ? (I have reflected the triangle.)

Please solve the question in comments with full working.

Please provide full working- If two angles are acute such that 2 sin(A+B) = root 3 and          
2 cos (A-B) = root 3 ; find the values of angles A and B.