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Two circles in rectangle5/18/2023 As an Amazon Associate I earn from qualifying purchases. (As you might expect, the links for my books go to their listings on Amazon. I am also the author of The Joy of Game Theory: An Introduction to Strategic Thinking, and several other books which are available on Amazon. I run the MindYourDecisions channel on YouTube, which has over 1 million subscribers and 200 million views. Then we substitute into the formula for the length of XY to get: This area is equal to 24, so we have r = 2. Thus half the rectangle’s area is also equal to:Ħ r/2 + 8 r/2 + 10 r/2 r(6 + 8 + 10)/2 12 r These three radii are the heights of 3 triangles, as shown below, and the sum of their areas is equal to half the rectangle. Construct three radii from circle X to the tangency points on the two sides and the diagonal. Since the rectangle has sides of 6 and 8, its diagonal is 10 (double a 3-4-5 right triangle). Half of the rectangle’s area is 6×8/2 = 24. The legs are then equal to 6 – 2 r and 8 – 2 r, so XY = √((6 – 2 r) 2 + (8 – 2 r) 2)Īll that remains is to solve for r. Construct a right triangle whose legs are the vertical and horizontal distances between X and Y and hypotenuse is equal to XY. Let r be the radius of the inscribed circles. (Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks).Ĭonstruct a vertical line through the center of circle X and a horizontal line through the center of circle Y, as shown below. Answer To Distance Between Two Inscribed Circles In A Rectangle MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon. "All will be well if you use your mind for your decisions, and mind only your decisions." Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. What is the distance between the centers of circles X and Y?Īs usual, watch the video for a solution.ĭistance Between Two Inscribed Circles In A Rectangle Inscribe circle X in one triangle and circle Y in the other triangle. Construct a diagonal of the rectangle, dividing the rectangle into two triangles. (rated 4.2/5 stars on 29 reviews) Kindle UnlimitedĪ rectangle has sides 6 and 8. Math Puzzles Volume 3 is the third in the series. Math Puzzles Volume 2 is a sequel book with more great problems. Volume 1 is rated 4.4/5 stars on 112 reviews. Math Puzzles Volume 1 features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. The puzzles topics include the mathematical subjects including geometry, probability, logic, and game theory. Mind Your Puzzles is a collection of the three “Math Puzzles” books, volumes 1, 2, and 3. Multiply Numbers By Drawing Lines This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. The Best Mental Math Tricks teaches how you can look like a math genius by solving problems in your head (rated 4.3/5 stars on 116 reviews) The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 4.3/5 stars on 290 reviews)Ĥ0 Paradoxes in Logic, Probability, and Game Theory contains thought-provoking and counter-intuitive results. The Joy of Game Theory shows how you can use math to out-think your competition. (1) The Joy of Game Theory: An Introduction to Strategic Thinking (2) 40 Paradoxes in Logic, Probability, and Game Theory (3) The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias (4) The Best Mental Math Tricks (5) Multiply Numbers By Drawing Lines Mind Your Decisions is a compilation of 5 books: If (circleDistance.x > (rect.width/2 + circle.If you purchase through these links, I may be compensated for purchases made on Amazon. Here is how I would do it: bool intersects(CircleType circle, RectType rect)ĬircleDistance.x = abs(circle.x - rect.x) ĬircleDistance.y = abs(circle.y - rect.y)
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