Question

Solve these guys..!!

Answer 1

12.

Let D be the midpoint of AB. Join CD.

Now, AB2 = BC2 + AC2 =

                 = BC2 + (√3BC)2

                 = BC2 + 3BC2

                = 4BC2

          AB =√(4BC2)

                = 2BC

Therefore AB = 2BC.  --- eq 1

Now, BD = 1/2 AB

               = 1/2(2BC)     (from eq 1)

               = BC.

But, D being the midpoint of hypotenuse AB, it is equidistant from all the

three vertices.

Therefore CD = BD = DA

                or  CD = 1/2 AB = BC.

Thus, BC = BD= CD,

i.e., △BCD is a equilateral triangle.

Hence, ∠ABC = 60°.