perplexus.info :: Shapes : Concentric Circles and a Chord

Concentric Circles and a Chord (Posted on 2023-07-19)

Two concentric circles are drawn with chord AB drawn on the larger circle.
AB cuts through the smaller circle at points C and D.
It is known that AC=7, CD=6, and DB=7.

What is the area between the two circles?

For comparison, the classic problem What's the area? is a version where the chord tangent to the inner circle.

See The Solution Submitted by Brian Smith

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

Solution

| Comment 2 of 7 |

Draw a perpendicular bisector to AB (passes through the center of the circles).

Connect each of A,B,C,D to the center.

The distance from the center to AB is d

d^2 + 3^2 = r^2

d^2 + 10^2 = R^2

Subtract: R^2 - r^2 = 10^2 - 3^2 = 91

The area in question is pi*R^2 - pi*r^2

The requested area is 91*pi

Posted by Larry on 2023-07-19 08:22:25

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info