I have a triangle circumscribed within a circle. One vertex is the exact center of the circle. To solve the question, I need to figure out the exact coordinates of the center point of the circle.
• $(x, y)$ and $(a, b)$ lie on the circumference of the circle.
• $(h, k)$ is the center of the circle.
• $(a, b)$ is known. $(x, y)$ and $(h, k)$ are unknown.
• $r$ is the radius of the circle. $r$ is known.
• $θ$ is the degrees of rotation that $(a, b)$ has been rotated clockwise from $(x, y)$.
• $θ$ is known.
• $u$ is unknown but can be calculated because the triangle is isosceles (which means the two remaining angles are congruent. Therefore $u / sinθ = r / sin((180 - θ) / 2)$. where $((180 - θ) / 2)$ is the formula used to get the degrees of either missing angle.
• (x, y) can be interpreted as (h, k + r).
Is it actually possible to find the center of the circle using the given information? I realize this isn't a standard geometry question, but real life applications of math rarely follow that format.