Grades 11-12 Video Solutions 2010-11&12 Video Solutions 2010 problem14

11&12 Video Solutions 2010 problem14

Video Transcription

Video Summary

The problem involves finding the area of a shaded region between two concentric circles. Given chord AB, tangent to the smaller circle, has a length of 16, the solution utilizes properties of tangency and the Pythagorean theorem. By forming a right triangle with the radius of the larger circle and half the chord length, the expression for the area of the shaded region is derived. Calculating \( R^2 - r^2 \) leads to \( 8^2 = 64 \). Substituting this into the area formula \( \pi(R^2 - r^2) \), the final area is \( 64\pi \), answer C.

Keywords

concentric circles

shaded region

tangency

Pythagorean theorem

area calculation