AD is a diameter of a circle and AB is a chord. If AB = 30cm and its perpendicular distance from the centre of the circle is 8cm, then what is the length of the diameter AD? Have a look on figure for details!
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consider the perpendicular from centre O to be OC
as perpendicular from centre bisects the chord
therefore OC bisects AB
so AC = BC = 15cm
as <ACO = 90°
therefore in ∆ACO, by Pythagoras theorem:
AO² = AC² + OC²
AO² = 15² + 8² = 225 + 64
AO = √289 = 17
therefore radius is 17 cm
diameter = 34 cm
as perpendicular from centre bisects the chord
therefore OC bisects AB
so AC = BC = 15cm
as <ACO = 90°
therefore in ∆ACO, by Pythagoras theorem:
AO² = AC² + OC²
AO² = 15² + 8² = 225 + 64
AO = √289 = 17
therefore radius is 17 cm
diameter = 34 cm
kakkar6644:
Thanks bro!! Correct Answer
no prob man
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Step-by-step explanation:
Radius- 17
Diameter-34
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