Question

If length of a chord of a circle is same as the length of the radius then the distance between the chord and the centre is​

Answer 1

Answer:

half of the radius's length.

Answer 2

Given :- If length of a chord of a circle is same as the length of the radius then the distance between the chord and the centre is ?

Solution :-

from image , we have,

• Let OA = OB = radius = r unit.
• AB = chord = radius = r unit .
• BP = AB/2 = (r/2) unit . { Line segment from centre to the chord , bisects the chord at 90° .}
• ∠OPB = 90° .

so, in right angled ∆OPB, we have,

→ OP² = OB² - PB²

→ OP² = r² - (r/2)²

→ OP² = r² - (r²/4)

→ OP² = (4r² - r²)/4

→ OP² = (3r²/4)

→ OP = (√3r/2)

→ OP = (√3/2)r unit.

therefore, the distance between the chord and the centre is (√3/2) times of radius of the circle.

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