The rectangle 5

The rectangle OABC has one vertex at O, the center of a circle, and a second vertex A is 2 cm from the edge of the circle, as shown. The vertex A is also a distance of 7 cm from C. The point 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:

AC=7 cm AC= d1 = d2 = r = diagonal = a2+b2  r=AC=7=7 cm
a + 2 cm = 7 a2 + b2 = 72  a=72=5 cm
b=r2a2=7252=2 6=4.899 cm

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