Grades 9-10 Video Solutions 2010-Levels 9&10 Video Solutions 2010 problem29

Levels 9&10 Video Solutions 2010 problem29

Video Transcription

Video Summary

The problem involves determining the radius of a larger arc within an oval inscribed in an 8 by 4 rectangle, with the oval exhibiting symmetry and comprising identical arcs. By establishing a right triangle using the centers of these arcs, the Pythagorean theorem is applied to solve for the radius \( R \) of the larger arc. Calculations reveal the triangle's sides and hypotenuse, leading to the algebraic equation \( (R - 1)^2 = 3^2 + (R - 2)^2 \). Simplification ultimately determines the radius \( R \) to be 6, providing the solution.

Keywords

oval

rectangle

Pythagorean theorem

radius

geometry