Omi67

1. Points $X$ and $Y$ lie on a circle centered at $O,$ and arc $XY$ is $80^\circ.$ The circle passing through points $O,$ $X,$ and $Y$ is drawn. Find the measure of arc $XOY$ on the smaller circle.

2. Trapezoid $WXYZ$ is inscribed in a circle, with $WX \parallel YZ$. If arc $YZ$ is $30$ degrees, arc $WZ$ is $t^2 + 7t$ degrees, and arc $XY$ is $60 - 4t$ degrees, find arc $WTX$.

Solve the system x/(x^2 + y^2) = 1 and y/(x^2 + y^2) = 2.

Solve for real x: 

I once calculated the red area. I hope that was your question.

???

ABCD is a square and K is the midpoint of BD.  E is on CK such that angle EDC = angle ECA.  What is the ratio of the area of trianlge AKE so the area of ABCD?

100 units - 90 units = 10 units

10/100=1/10

Do jou need the red area?

(sqrt(x) - 1)*sqrt(x)*(sqrt(x) + 1)   = 6

                                               x   = 4

(sqrt(4) - 1)*sqrt(4)*(sqrt(4) + 1) = 6

                          (2 - 1)*2*(2 + 1) = 6

                                          1*2*3 = 6

Two circles, each with radii 900, are tangent to each other and they are both tangent to a line. Find the radius of the circle which is tangent to both circles and also the line.

For what values of $j$ does the equation $(2x+7)(x-5) = -43 + jx$ have exactly one real solution? Express your answer as a list of numbers, separated by commas.

Ja, die Umformung ist erlaubt