Question

find the area of segment of a circle with radius 8 cm and the central angle is 90 degree​

Answer 1

Answer:

201.06cm^2

Explanation:

use the formula of area of circle

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Answer 2

Answer:

Proof:

Consider the alternate angle ACD (as x) is equal to the angle ABC is shown on the other side of the chord, where DC is the tangent to the circle.

Triangle ABC has points A,B and C on the circumference of a circle with centre O. Join points OA and OC to form triangle AOC.

Let ∠ACD = x, and ∠OCA = y.

We know that tangent to a circle is at a right angle to the radius of a circle,

Therefore, x+y=90° ——————————(i)

Bisect the triangle AOC from the point O, then the triangle formed is a right-angled triangle at E. Let the bisected angle be z.

Therefore, ∠AOE = ∠COE =z

Sum of angles of a triangle is 180°

In △COE, y+z+90° = 180°

Or, y+z = 90° —————————(ii)

Equating equation (i) and (ii), we have

x = z

We know, ∠ABC = ∠ACD = x

Therefore, ∠AOC = 2z

and ∠ABC = x

Which implies ∠AOC = 2∠ABC

Explanation: