Question

h is the circumcenter of δace. what is the length of $overline{ha}$? 7 units 8 units 24 units 48 units

Explanation:

Step1: Recall circum - center property

The circum - center of a triangle is equidistant from the vertices of the triangle. So, \(HA = HC\).
Set up the equation \(2x + 32=6x\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(32 = 6x-2x\), which simplifies to \(32 = 4x\).
Divide both sides by 4: \(x=\frac{32}{4}=8\).

Step3: Find the length of \(HA\)

Substitute \(x = 8\) into the expression for \(HA\) (we can use either \(2x + 32\) or \(6x\)). Using \(6x\), when \(x = 8\), \(HA=6\times8 = 48\) units.

Answer:

48 units