Math, asked by aryankanumuri05, 4 months ago

proper explanation and I mark brainliest:)​

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Answers

Answered by joelpaulabraham
2

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.

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