Question

in the figure to the right, if ac = 19 and bc = 16, what is the radius? the radius is approximately 24.84. (round to the nearest tenth as needed.)

Explanation:

Step1: Apply Pythagorean theorem

Let radius $AB = AD = r$. Then $AC^{2}=BC^{2}+AB^{2}$. Substitute $AC = 19$ and $BC = 16$: $19^{2}=16^{2}+r^{2}$.

Step2: Solve for r

$r^{2}=19^{2}-16^{2}=(19 + 16)(19 - 16)=35\times3 = 105$. So $r=\sqrt{105}\approx10.2$.

Answer:

$10.2$