Geometry Practice Test 1

Radius, r = a cm
In ΔXZY,
${\left(\mathit{X}\mathit{Z}\right)}^2+{\left(\mathit{Z}\mathit{Y}\right)}^2$ = ${\left(\mathit{X}\mathit{Y}\right)}^2$
${\left(6+\mathit{a}\right)}^2+{\left(3+\mathit{a}\right)}^2$ = ${\left(15\right)}^2$
36 + ${\mathit{a}}^2$ +12a + 9 + ${\mathit{a}}^2$ + 6a = 225
$2{\mathit{a}}^2$ +18a −180 = 0

${\mathit{a}}^2$ + 9a − 90 = 0
${\mathit{a}}^2$ +15a − 6a − 90 = 0
a(a +15)− 6(a +15) = 0
(a − 6) (a +15) = 0
a = 6 radius