Question

point y is the circumcenter of δdef. find fy. 5 11 17 22 f 3x + 7 n 5x - 3 e

Explanation:

Step1: Recall circum - center property

The circum - center of a triangle is equidistant from the vertices of the triangle. So, $FY = EY$. Set up the equation $3x + 7=5x - 3$.

Step2: Solve the equation for $x$

Subtract $3x$ from both sides: $7 = 5x-3 - 3x$, which simplifies to $7 = 2x - 3$. Then add 3 to both sides: $7 + 3=2x$, so $10 = 2x$. Divide both sides by 2, we get $x = 5$.

Step3: Find the length of $FY$

Substitute $x = 5$ into the expression for $FY$ which is $3x + 7$. So, $FY=3\times5 + 7=15 + 7=22$.

Answer:

22