Geometry Practice Test 3

We have a circle with radius 5 cm.
PQ = 6 cm
Length of TP = x
By using Pythagoras theorem,
ΔPMO
${\left(\mathit{O}\mathit{M}\right)}^2+{\left(\mathit{P}\mathit{M}\right)}^2$ = $\mathit{O}{\mathit{P}}^2$
${\left(3\right)}^2\mathit{O}{\mathit{M}}^2$ = ${\left(5\right)}^2$
OM = $\sqrt{25-9}$
OM = $\sqrt{16}$ = 4 cm
Let ∠POM = Q Let TP = x

Using Trigonometric ratio on ΔPMO and ΔPOT,
we get
tan θ = $\frac{3}{4}$
tan θ = $\frac{\mathit{x}}{5}$
$\frac{3}{4}$ = $\frac{\mathit{x}}{5}$
x = $\frac{15}{4}$ = 3.75 cm