Line AB intersects circle c at points a and b, as shown, and is 12 cm long. If line AB is 2cm from the center of the circle c, what is the radius of circle c to the nearest tenth of a centimeter.
Accepted Solution
A:
Answer: The radius of circle with center c is 6.3 cmStep-by-step explanation:Given as :For a circle , The line AB intersects circle at a , bThe length of AB = 12 cm The distance of AB from the center of circle c = 2 cmLet The radius of circle = r cmNow , Since , AB intercept on circle , so the length from center divide the intercept equally I.e AD = DB = 6 cm. and the length will make right angle on ABSo, radius from center c to the point b is r∴ r = BD + cDOr, r² = BD² + cD² Or, r² = 6² + 2² Or, r² = 36 + 4 Or, r² = 40∴ r = [tex]\sqrt{40}[/tex] = 6.324 cmI,e r = 6.3 cmHence The radius of circle with center c is 6.3 cm Answer