# Geometry

posted by .

Find the area of a segment formed by a chord 8" long in a circle with radius of 8".

• Geometry -

as we all know, the side of an inscribed hexagon is equal to the radius.

So, the angle subtending the side is π/3

a = 1/2 r^2 (θ - sinθ)
= 1/2 * 64 (π/3 - √3/2)
= 32/6 (2π - 3√3)

More generally, the angle θ which subtends a chord of length s in a circle of radius r is

sin θ/2 = (s/2)/r = s/2r

In this problem, s=r=8, so

sin θ/2 = 1/2
θ = π/3

and away we go.

## Similar Questions

1. ### geometry

suppose the diameter of a circle is 20in. long and a chord is 16in. long. What is the distance from the center of the circle to the chord Draw a radius from the center to the end of the chord. THe draw a radius from the center perpendicular …
2. ### Geometry

How would you solve these? The radius of a circle is 34 meters long, and a chord of the circle is 60 meters long. How far is the chord from the center of the circle?
3. ### geometry

Express answer in exact form. Find the area of the smaller segment whose chord is 8" long in a circle with an 8" radius
4. ### geometry

Find the area of the smaller segment whose chord is 8" long in a circle with an 8" radius. (3.14) A=( pie - / )inches^2 please help me i don't understand this problem
5. ### pre-calculus

find the area of the segment formed by a chord 24 cm long in a circle of radius 13 cm.
6. ### geometry

Answer has to be in exact form.Find the area of a segment formed by a chord 8" long in a circle with radius of 8".
7. ### Maths

AB is a chord with centre O and radius 4 cm. AB is of length 4 cm and divides the circle into two segments. Find d area of minor segment. A chord PQ of length 12cm suntends an angle of 120 degree at the centre of a circle. Find the …
8. ### math geometry

Given a circle with an 8" radius, find the area of the smaller segment whose chord is 8" long?
9. ### Geometry

A chord PQ of a circle with radius r subtends an angle B at the center. Show that the area of the minor segment PQ=1/2.r^2.(B-sinB) and write down the area of the major segment PQ interms of r and B.
10. ### Geometry

Express answer in exact form. Find the area of the larger segment whose chord is 8" long in a circle with an 8" radius. (Hint: A chord divides a circle into two segments. In problem 1, you found the area of the smaller segment.) I've …

More Similar Questions