Dragan

When a quadrilateral is inscribed in a circle, the sum of the opposite angles is 180º!!!

Angle  a = 110º / 2 = 55º

Angle  b = 180º - 55º = 125º  

Triangle WXY has side lengths XY = 14 and WX = 8. The tangent to the circumcircle of triangle WXY at X is drawn, and the line through W that is parallel to this tangent intersects XY at Z. Find YZ. 

Hint:::    Use the right-angled triangle with legs of 8 and 14  

*** No matter what type of a triangle is used, the result will be the same!!! ***

The radius CANNOT  be 7 units !!!

r = [sqrt( 13² + 1² )] / 2 = 6.519202405 units  

The area of the shaded region:>               A = ( r²pi ) - (7² + 6²) / 2 = 91.0176878 u² 

6x +8 + 4x + 2 = 180        solve for x

There's a shortcut:::

Important:   The ratio of  QO  to  NO is  2 : 1        ( The Median Theorem )

NR = 1/2 * 14 = 7            ( QN ⊥ PR )

NO = 1/3 * 12 = 4

OR = sqrt (7² + 4²) = √65 

Hint:   connect points T, A, and U to the center of a circle. 

You should be able to solve it now.

AB = 12        BD = 6

AD = sqrt[( AB)²- ( BD)²]

BE = sqrt[( BD)²+(AD/2)²]

A right triangle has two sides of length 6 units each. What is the area of the triangle, in square units?

You can find the answer here:::   https://web2.0calc.com/questions/please-help_66642#r2

The image below with two squares, ABCD and BFGE, sharing a vertex. Given that AE = 5, what is the length of DG?

AB = 12         BE = 8          AX = 4