The radii of two concentric circles are 15 cm
and 20 cm. A line segment ABCD cuts the
outer circle at A and D and inner circle at B
and C. If BC = 18 cm, find the length of AB.
Answers
AB = 7 cm if A line ABCD intersect two concentric circles of 15cm & 20 cm Radius cut outer circle at A & D & inner Circle at B & C . BC = 18 cm
Step-by-step explanation:
A line segment ABCD cuts the outer circle at A and D and inner circle at B
and C
=> AD & BC are chord of corresponding circle
Now let say O is center of both circles as concentric circles
now draw OP ⊥ AD / BC
Perpendicular on chord bisect chord
=> BO = BC/2 = 18/2 = 9 cm
in Δ BOP
OP² = BO² - BP²
BO = Radius of inner circle = 15 cm
=> OP² = 15² - 9²
=> OP² = 144
=> OP = 12 cm
in Δ AOP
AP² = AO² - OP²
AO = Radius of outer circle = 20 cm
=> AP² = 20² - 12²
=> AP² = 256
=> AP =16 cm
AB = AP - BP
=> AB = 16 - 9
=> AB = 7 cm
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