Question

what is segment of a circle and how to find its area?​

Answer 1

Answer:

The formula to find the area of the segment is in photo . It can also be found by calculating the area of the whole pie-shaped sector and subtracting the area of the isosceles triangle ABC

Answer 2

$\huge\star{\red{\underline{\mathfrak{Answer :-}}}}$

Segment :-

A segment of a circle is an area bounded by a chord and the corresponding arc.

In the given photo, the area shaded in blue who is the segment APB.

This segment can also be called as minor segment because it is bounded by chord AB and minor arc APB.

In the figure, we can also say that segment AQB is major segment because it is bounded by chord AB and the arc AQB.

Formulas related to segment :-

There three formulas to find the area of the segment.

1) Formula 1 :-

$\boxed{\green {ar ( segment ) = ar( sector ) - ar ( Triangle )}}$

From the given figure, the above formula can be simplified into :-

Area of segment APB = Area of sector AOBP - Area of triangle AOB

2)Formula 2 :-

If the theta angle given is equal to or less than 90 degrees, then the following formula can be used :-

$\boxed {\green{\frac{\pi {r}^{2} \theta}{360} - \frac{ {r}^{2} \sin(\theta) }{2} }}$

3)Formula 3 :-

If the theta angle given is more than 90 degrees, then the following formula can be used :-

$\boxed {\green{ \frac{\pi {r}^{2}\theta}{360} - {r}^{2} \sin( \frac{\theta}{2} ) \cos( \frac{\theta}{2} )}}$

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