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Answers
Answer:
AB = 2√(R² - 9), where R is the radius of the circle.
Step-by-step explanation:
Given:-
A circle with centre O, OC is a line drawn perpendicular to the chord AB, through the centre O.
OC = 3cm
To Find:-
chord AB
Proof:-
In Circle with centre O, if a line is drawn perpendicular to any chord which passes through the centre O, the line bisects the chord.
Thus,
AC = BC
Now,
Let the radius of the Circle be R,
So,
OB = R
Now,
OB = R
OC = 3 cm
∠OCB = 90°
Hence, it is a right triangle,
So, by using Pythagoras theorem,
OC² + BC² = OB²
3² + BC² = R²
BC² = R² - 3²
BC² = R² - 9
BC = √(R² - 9)
Now,
AB = AC + BC
Since, AC = BC
AB = BC + BC
AB = 2BC
So, putting in the value,
AB = 2 × √(R² - 9)
AB = 2√(R² - 9)
Hence,
AB = 2√(R² - 9), where R is the radius of the circle.
Hope it helped.