Question

Points a and b are on a circle of radius 5 and ab = 6. Point c is the midpoint of the minor arc ab. What is the length of the line segment ac?

Answer 1

Given : Points a and b are on a circle of radius 5 and ab = 6. Point c is the midpoint of the minor arc ab

To find : length of the line segment ac  

Solution :

ab = 6

radius = 5

let say O is the center of circle

then oa = ob = oc = 5

c is the mid point of ab

hence oc will intersect ab at M such that

am = bm = ab/2 =  6/2 = 3

=> om² = oa² - am²

=> om² = 5² - 3²

=> om² = 16

=> om = 4

=> cm = oc - om = 5 -4  = 1  cm

am = 3 cm

ac² = am² + cm²

=> ac² = 3² + 1²

=> ac² = 10

=> ac = √10

length of the line segment ac  = √10

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