Question

In triangle $ABC,$ $AB = BC = 17$ and $AC = 16.$ Find the circumradius of triangle $ABC.$

Answer 1

Answer:

$R = 9.63\ units$

Step-by-step explanation:

Given

$AB = BC = 17$

$AC = 16$

Required

Determine the circumradius, R

The circumradius is calculated as follows;

$R = \frac{AB * BC * AC}{\sqrt{(AB + BC + AC)(AB + BC - AC)(AB + AC - BC)(AC + BC - AB)}}$

Substitute the values of AB, BC and AC

$R = \frac{17 * 17 * 16}{\sqrt{(17 + 17 + 16)(17 + 17 - 16)(17 + 16 - 17)(16 + 17 - 17)}}$

Evaluate the denominator

$R = \frac{17 * 17 * 16}{\sqrt{(50)(18)(16)(16)}}$

$R = \frac{4624}{\sqrt{230400}}$

Take square root of 230400

$R = \frac{4624}{480}$

$R = 9.63\ units$ (Approximated)

Hence, the circumradius is 9.63