Question

given that point h is the circumcenter of △xyz, what is the length of yh? 2√10 √10 4√10 3√10

Explanation:

Step1: Recall circum - center property

The circum - center of a triangle is equidistant from the vertices of the triangle. Consider right - triangle $\triangle YUH$.

Step2: Identify right - triangle sides

In right - triangle $\triangle YUH$, $YU = 6$ and $UH = 2$.

Step3: Apply Pythagorean theorem

By the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 2$, $b = 6$, and $c=YH$. So $YH=\sqrt{2^{2}+6^{2}}=\sqrt{4 + 36}=\sqrt{40}=2\sqrt{10}$.

Answer:

A. $2\sqrt{10}$