MHB How Do Circles and Parallel Lines Interact in Geometry?

AI Thread Summary
The discussion focuses on solving a geometry problem involving circles and parallel lines. A user expresses confusion about calculating areas related to shaded and unshaded regions. Another participant clarifies that the problem can be simplified by canceling out corresponding areas, leading to a straightforward solution of 32 cm² for the difference between the two areas. The interaction highlights the collaborative nature of the forum in helping users understand geometric concepts. Overall, the exchange emphasizes the importance of breaking down complex problems into manageable parts.
wailingkoh
Messages
18
Reaction score
0
Hi all,

Please help. I am stuck with the question below and I have no clue how to solve:

View attachment 4573

Thanks for the help.
 

Attachments

  • wailingkoh01.jpg
    wailingkoh01.jpg
    26.5 KB · Views: 116
Mathematics news on Phys.org

Attachments

  • areas.png
    areas.png
    4 KB · Views: 116
Hi
Thanks for the reply. Do I solve it by fraction. Sorry, I am very lost with this question
 
8 multiply by 4 for 32 units square but I still won't get the full shaded and unshaded
 
You don't need them. "Cancelling" the dotted areas with their corresponding shaded areas leaves a dotted rectangle which is 32 cm. squared. That's the difference between the two areas.
 
Awesome!
I was so silly.

Thanks for the help.

This forum is great
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Thread 'Six Pencil Puzzle'

Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
View full post »

Similar threads

B Existence of parallels in axiomatic plane geometries
Replies
36
Views
5K
MHB Find the area of the shaded region
Replies
2
Views
1K
MHB How Can I Find the Equation of the Dotted Tangent Line of a Circle?
Replies
5
Views
2K
I Relation between a circle and line in complex plane
Replies
16
Views
2K
MHB [ASK] A Line Intercepting A Circle
Replies
4
Views
1K
MHB Tangent line to circle making 30º with a second circle
Replies
2
Views
2K
B Inscribing a circle in an Oblique Square (Drafting)
Replies
9
Views
1K
MHB Finding the Center of a Circle
Replies
3
Views
1K
MHB Find the points of intersection of a line and a circle
Replies
2
Views
1K
MHB Slope Intercept Equation with parallel
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top