As posed, I fear there is no unique answer to this question.
Look at this webpage.
I think that you need to know the radius of one of those two circles. Or some other term from that webpage.
I have no idea how to solve this. I love geometry, but I've found that I'm not very naturally good at it. please help!
The circles in the figure I have drawn out are concentric. The chord AB is tangent to the inner circle and has a length of 12 cm. What is the Area of of the non-shaded region? (A of big triangle - A of small triangle)
As posed, I fear there is no unique answer to this question.
Look at this webpage.
I think that you need to know the radius of one of those two circles. Or some other term from that webpage.
Hello, aaronrpoole!
This is a classic problem . . . with a surprising punchline.
The circles in the figure I have drawn are concentric.
The chord AB is tangent to the inner circle and has a length of 12 cm.
What is the area of of the non-shaded region? (Area of big circle - Area of small circle)
Code:* * * * * * C 6 * A *- - - - ♥ - - - -♥ B * | * o * * r| o* R * * * ♥ * * * * O * * * * * * * * * * * * * *
is the center of the circles.
is the midpoint of chord
Let , the radius of the large circle.
Let , the radius of the small circle.
From right triangle .[1]
The area of the large circle is:
The area of the small circle is:
The area of the ring is:
Substitute [1]: .
Surprise! .We didn't need to know the two radii.
The small circle could be a golfball or the Earth.
The area of the ring is constant!
While this subject can be very touchy for most people, my opinion is that there has to be a middle or common ground that we all can find. I do appreciate that youve added relevant and intelligent commentary here though. Thank you!