Can someone solve with a system of equations and show work?

  1

Step-by-step explanation:

Label the points as in the attachment. Then we have ...

We can form the sum P + R + T and we get ...

  P +R +T = (a+b)/2 +(c+d)/2 +(e+a)/2 = a +(b +c +d +e)/2

We can form the sum Q + S and we get ...

  Q + S = (b+c)/2 +(d+e)/2 = (b +c +d +e)/2

Subtracting the latter sum from the former one gives ...

  P +R +T -(Q +S) = a +(b +c +d +e)/2 -(b +c +d +e)/2 = a

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So, the value picked by the person with the average "6" was ...

 (7 +1 +5) -(9 +3) = 13 -12 = 1

The person with average "6" picked 1.

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The system of equations written in matrix form is shown in the second attachment. The inverse of the coefficient matrix is shown in the third attachment. That is where the sum shown above came from.

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The rest of the picked numbers are ...

  P = 2, b = 13, Q = 14, c = 5, R = 6, d = -3, S = -2, e = 9, T = 10

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.