Grades 9-10 Video Solutions 2023-2023_9-10

Video Transcription

Video Summary

The transcript describes a problem involving two touching semicircles with parallel diameters and calculates the square of the distance AD using geometry. The centers of the circles are separated by a distance of 2, corresponding to the sum of their radii. By forming right triangles within this setup, the Pythagorean theorem is applied: \( x^2 = 1^2 + (2 + \sqrt{3})^2 \). Simplifying, the square of the distance AD is calculated as \( 8 + 4\sqrt{3} \). Therefore, the answer to the problem is \( 8 + 4\sqrt{3} \).

Keywords

semicircles

geometry

Pythagorean theorem

distance calculation

right triangles