STEM Geometry Challenge 1597: Circle-Triangle Intersection Problem
Apply Science, Technology, Engineering, and Math (STEM) principles to solve this elegant geometry puzzle. Perfect for Olympiad training and critical thinking practice!
Problem 1597 Statement
In triangle ABC, the lengths are given as BC = 7 and AC = 8. A circle centered at C with radius BC intersects side AB at point D, such that BD = 2. A second circle is drawn with diameter AD, intersecting AC at point E. Determine the length of segment CE.
Circles intersect
Lines and angles tell their truth
Solution awaits
STEM Approach to the Geometry Problem 1597
Using a STEM approach in solving this geometry problem 1597 adds significant educational value and engagement potential.
Science (S)
Analytical Thinking
The problem involves observing geometric relationships and forming hypotheses
like
"Could the elegant Pythagorean theorem unlock this secret, or perhaps the subtle
Power of a Point?". It encourages experimentation with different
methods such as coordinate geometry, trigonometry, or pure Euclidean geometry.
Technology (T)
Tools & Visualization
Solvers might use tools like Geogebra, Desmos, Geometry Expressions, or the
Wolfram Demonstrations Project to visualize the problem, linking
math and technology. Digital tools help verify solutions, making abstract
concepts tangible almost touch and feel.
Engineering (E)
Problem-Solving & Optimization
Like engineers, solvers break the problem into smaller steps: find AB, use
circle
properties for AD, perhaps employing the Pythagorean theorem to locate E, and
finally, calculate CE — This methodical breakdown mirrors the systematic
approaches that drive innovation in the real world.
Mathematics (M)
Core Discipline
Pure geometry, intertwined with algebra, and multi-method solving (trigonometry,
coordinate, synthetic geometry)
are at the heart of this problem, showcasing math’s versatility and its profound
depth, offering not just one solution, but a tapestry of interconnected ideas.
STEM Geometry Challenge 1597: Unlock the Power of Problem-Solving!
