If `Delta` stands for the operation `text('adding first number to twice the second number'),` then find the value of `(1\ Delta\ 2)\ Delta\ 3.`

Find the total number of triangle in the given diagram.

If 21 is added to the number first number of two given numbers, it becomes twice the second number and if 12 is added to the second number, it becomes twice the first number. Find the numbers.

If Delta be area of incircle of a triangle ABC and Delta_1,Delta_2,Delta_3 be the area of excircles then find the least value of (Delta_1 Delta_2 Delta_3)/(729 Delta^3)

If the angles of a triangle are in the ratio of 1:2:3 , then find the value of the largest angle

Find the number of triangle a in the following figure :

If Delta is an operation such that for integers a and b we have a Deltab=axxa+bxxb-axxb , then find (-3) Delta 2.

Given a triangle ABC with AB= 2 and AC=1 . Internal bisector of angleBAC intersects BC at D. If AD = BD and Delta is the area of triangle ABC, then find the value of 12Delta^2 .