Grades 11-12 Video Solutions 2012-2012_11-12

Video Transcription

Video Summary

The radius \( R \) of the inscribed semicircle in a right triangle with sides \( a \), \( b \), and \( c \) can be found using the properties of similar triangles. By setting up a proportion between the original triangle and a smaller right triangle formed by the tangent and radius, we find \( \frac{a}{c} = \frac{R}{b-R} \). Solving for \( R \) involves cross-multiplying and simplifying the equation to derive \( R = \frac{ab}{a + c} \). This formula provides the radius of the inscribed semicircle within the right triangle.

Keywords

inscribed semicircle

right triangle

radius formula

similar triangles

proportion