The rectangle 5

The rectangle OABC has one vertex at O, the center of a circle, and a second vertex, A, 2 cm from the edge of the circle, as shown. The vertex A is also 7 cm from C. The points B and C lie on the circumference of the circle.

a. What is the radius?
b. Find the length of AB.

Correct answer:

r =  7 cm
a =  5 cm
b =  4.899 cm

Step-by-step explanation:

$$\begin{gathered} AC=7\text{cm} \\ AC=d_1=d_2=r=diagonal=\sqrt{a^2+b^2} \\ r=AC=7=7\text{cm} \end{gathered}$$

$$\begin{gathered} a+2cm=7 \\ {a}^2+b^2=7^2 \\ a=7-2=5\text{cm} \end{gathered}$$

$b=\sqrt{r^2-a^2}=\sqrt{7^2-5^2}=2\sqrt{6}=4.899\text{cm}$

Try another example