Dragan

That question is for that guest who cannot solve that simple question. 

Yes! If you need to find the area of an incircle, you need only a radius of that circle. But if you need to find the area of a circumcircle, you need to find the lengths of both radii. 

You're very welcome!

XOY is a quarter-circle. Semicircles are drawn with diameters OX and OY as shown. Find the area of the shaded region given that XO

Important:::  If the value of scale factor k is negative, the dilation takes place in the opposite direction from the center of dilation on the same straight line containing the center and the pre-image point.

A / [xyz] = 0.407407407 = 11/27  

If the radius of a larger circle is increased, the ratio of AB to PA  does not change! 

1)   Find the perimeter         P = a + b + c

2)   Find semiperimeter       s = ( a + b + c ) / 2

3)   Find area                       A = sqrt [ s( s-a )( s-b )( s-c )]       ( Heron's formula )

4)   Calculate inradius          r = A / s

5)    Calculate circumradius     R = ( abc ) /4rs

6)    Inner angles                    a² = b² + c² - 2bc * cos(A)         ( The law of cosines ) 

I hope it covers everything you wanted to know. 

Area of 3 segments if the radius is 1        A_3segments = ( r²pi - 3√3 / 2 ) / 2            r = a = 1

Red area                                    A = (√3 / 4) + ( r²pi - 3√3 / 2 ) / 2  

This is very simple!!! Your 'stuckness' will disappear in a minute.

∠AOB = ∠COB = 90º

1st      Find an angle  AOC          ∠AOC = ∠AOB + ∠COB

                                                     ∠AOC = 2[arccos( AO / OB )] = 108.6293306º

2nd     Find the central angle of a major arc ADC

                 That angle is    360º - ∠AOC = 251.3706694º

3rd       Find the length of ADC

                                         ADC = 2 * 7 * pi * ( 251.3706694 / 360 ) = 30.711

Btw, I have confidence in my 1%