I got reference of this Puzzle from Twitter. I uploaded two of its possible and easy solutions. You may line this Puzzle.
So, dare to solve it...
Take a look at figure given below. Give it a try and when you are ready then watch the solution.
This is a moderate level puzzle. But the condition is you have to know some basic concepts.
Solution:
Perimeter of this figure = arc ADC + AB + CB
First you have to draw OA line.
We have AB = 12cm.
By the concept of angle inscribed by to points on circle with respect to third point on same circle is half the angle formed by same two points and center:
Angle AOB = 2 times Angle ADO
Angle AOB = 90
As we can see, AOB is an 30-60-90 triangle.
AO and OC are radius of circle.
AO = AB cos(60)
AO = 12/2
AO = 6
⇒ Radius (r) = 6
As we can observe,
arc ADC cover 3/4 of circle:
arc ADC = (3/4)*2πr
arc ADC = 9π
Now,
OB = 12(√3/2)
OB = 6√3
CB = OB-OC
CB = 6√3-6
Now,
Perimeter of this figure = arc ADC + AB + CB
Perimeter of this figure = 9π+12+6√3-6
Perimeter of this figure = 9π+6√3+6
