A chord with a length of $5$ $5$ runs from $\frac{π}{8}$ $pi/8$ to $\frac{π}{3}$ $pi/3$ radians on a circle. What is the area of the circle?

Question

A chord with a length of $5$ $5$ runs from $\frac{π}{8}$ $pi/8$ to $\frac{π}{3}$ $pi/3$ radians on a circle. What is the area of the circle?

1 Answer

Impact of this question

1512 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-07T02:23:23

Area of circle $A = 190.0334$ $color(blue)(A = 190.0334$

Explanation:

enter image source here

Length of chord $A B = 5$ $AB = 5$

$A M = \frac{A B}{2} = \frac{5}{2}$ $AM = (AB)/2 = 5/2$

Angle subtended by the chord 5 at the center = $∠ (A O M) = θ$ $/_(AOM) = theta$

Given $θ = \frac{π}{3} - \frac{π}{8} = \frac{5 π}{24}$ $theta = pi/3 - pi/8 = (5pi)/24$

$∠ (A O M) = \frac{θ}{2} = \frac{5 π}{48}$ $/_(AOM) = theta / 2 = (5pi)/48$

In right angle triangle AOM,

$O A = r = \frac{A M}{sin (\frac{θ}{2})}$ $OA = r = (AM) / sin ((theta)/2)$

$r = \frac{\frac{5}{2}}{sin (\frac{5 π}{48})} = \frac{5}{2 \cdot sin (\frac{5 π}{48})} = 7.7775$ $r = (5/2) / sin ((5pi) / 48) = 5 / (2 * sin ((5pi)/48)) = 7.7775$

Area of the circle $A_{c} = π r^{2} = π \cdot {(7.7775)}^{2}$ $A_c = pi r^2 = pi * (7.7775)^2$

Area of circle $A = 190.0334$ $color(blue)(A = 190.0334$

Science

Math

Humanities

... and beyond

A chord with a length of $5$ $5$ runs from $\frac{π}{8}$ $pi/8$ to $\frac{π}{3}$ $pi/3$ radians on a circle. What is the area of the circle?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A chord with a length of 5 55 runs from pi/8 π8pi/8 to pi/3 π3pi/3 radians on a circle. What is the area of the circle?

1 Answer

Explanation:

Related questions

Impact of this question

A chord with a length of $5$ $5$ runs from $\frac{π}{8}$ $pi/8$ to $\frac{π}{3}$ $pi/3$ radians on a circle. What is the area of the circle?