The Trick Is NOT What You Think… Find the Radius
Mathpiad
33,762 views
Can you find the radius of a circle when all you’re given is a triangle inside it? In this geometry challenge, we solve a tricky circle and triangle problem using the Pythagorean theorem, algebraic simplification, Thales’ theorem, and similar triangles.
We are given triangle PQR with side lengths 10, 17, and 21 units, and our goal is to find the radius of its circumscribed circle. The solution begins by drawing an altitude, introducing an unknown X, and using two right triangles to uncover the hidden height. Then we use a clever diameter construction and similar triangles to calculate the circle’s diameter and finally its radius.
You’ll learn how to recognize hidden right triangles, expand a squared binomial, simplify algebraic equations, apply Thales’ theorem, identify corresponding angles, and use triangle similarity to solve a geometry problem efficiently.
This is a great problem for students studying geometry, algebra, SAT and ACT math, GCSE, A-Level, high school mathematics, and competitive math. If you enjoy challenging geometry problems and learning the reasoning behind every step, this solution is designed to make the entire process clear and easy to follow.
Like the video if you found the geometry trick useful, subscribe for more challenging math problems, and comment your answer before watching the full solution!
#Geometry #MathProblem #GeometryChallenge #MathTricks #Mathematics
20 Comments
😀😀 For a triangle with side lengths 10 17 and 21 first find the area using Herons formula. The semiperimeter is 24 so the area is sqrt of 24 times 14 times 7 times 3 which is 84. Then use the circumradius formula R equals abc divided by 4K. So R equals 10 times 17 times 21 divided by 4 times 84 which is 10.625. Therefore the circumradius is 10.625 and the diameter is 21.25.
Beginners will benefit hugely from your step-by-step approach. You go from the given to the final answer and clearly show how and why the math works.
2Rsinx=21, where x is the angle opposite 21. R=10.625.
that states, 4R^2= each chord segment squared; 4R^2=8^2+(45/4)^2+6^2+15^2. Solve for R = 10.625.
The Trick Is NOT What You Think… Find the Radius
Mathpiad
33,762 views
Can you find the radius of a circle when all you’re given is a triangle inside it? In this geometry challenge, we solve a tricky circle and triangle problem using the Pythagorean theorem, algebraic simplification, Thales’ theorem, and similar triangles.
We are given triangle PQR with side lengths 10, 17, and 21 units, and our goal is to find the radius of its circumscribed circle. The solution begins by drawing an altitude, introducing an unknown X, and using two right triangles to uncover the hidden height. Then we use a clever diameter construction and similar triangles to calculate the circle’s diameter and finally its radius.
You’ll learn how to recognize hidden right triangles, expand a squared binomial, simplify algebraic equations, apply Thales’ theorem, identify corresponding angles, and use triangle similarity to solve a geometry problem efficiently.
This is a great problem for students studying geometry, algebra, SAT and ACT math, GCSE, A-Level, high school mathematics, and competitive math. If you enjoy challenging geometry problems and learning the reasoning behind every step, this solution is designed to make the entire process clear and easy to follow.
Like the video if you found the geometry trick useful, subscribe for more challenging math problems, and comment your answer before watching the full solution!
#Geometry #MathProblem #GeometryChallenge #MathTricks #Mathematics