In a circle, from one point of the circle, two chords are drawn at an angle of 90 to each other

| April 30, 2021 | education

In a circle, from one point of the circle, two chords are drawn at an angle of 90 to each other. find the area of the part of the circle enclosed between them, if the length of each chord is 4 cm.

Since the angle between the chords is 900, this angle is based on the diameter of the circle.

The ABC triangle is equilateral and rectangular, then, according to the Pythagorean theorem, AC ^ 2 = AB ^ 2 + BC ^ 2 = 16 + 16 = 32.

AC = √32 = 4 * √2 cm.

Then ОА = R = (4 * √2) / 2 = 2 * √2 cm.

Determine the area of ​​the circle.

Scr = n * R2 = n * (2 * √2) 2 = n * 8 cm2.

Determine the area of ​​half a circle bounded by its diameter. S = Scr / 2 = n * 4 cm2.

Determine the area of ​​the triangle ABC. Savs = AB * BC / 2 = 4 * 4/2 = 8 cm2.

Let us determine the area of ​​the sector bounded by the chords AB and BC.

Ssec = S + Savs = n * 4 + 8 = 4 * (n * 2) cm2.

Answer: The area of ​​the sector is 4 * (n * 2) cm2.



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