Lesson Plans SET B for Grades 9-10-Lesson 8 Level 9-10

Lesson 8 Level 9-10 - HW

Pdf Summary

The document is a Level 9-10 geometry homework set focused on circles, provided for Math Kangaroo students. The set comprises five problems centered around circle properties, involving geometric figures like triangles, squares, and line segments, all related to circles.<br /><br />1. **First Problem:** It involves calculating the radius of a circle by forming a right triangle with given side lengths related to the circle. The solution includes using the Pythagorean theorem to find the radius as 5.<br /><br />2. **Second Problem:** The task is to determine a circle's radius with given line segments AB=8 and BC=4, where O is the circle’s center. The solution uses the circle’s chord properties and results in a radius of 5.<br /><br />3. **Third Problem:** This involves two identical tangent circles (radius 10) and a square intersecting them. The problem is to find the area of the square. After setting an algebraic equation based on the circle and square properties, the side length of the square is found to be 4, leading to an area of 16 square units.<br /><br />4. **Fourth Problem:** A square with a side of 4 and two quarter circle arcs is given, and the shaded region formed by these arcs within the square must be computed. By calculating and subtracting relevant areas, the shaded area is determined to be 16.<br /><br />5. **Fifth Problem:** Here, three circles are inscribed in a square, with two congruent red circles and one blue circle. The task is to find the ratio between the radii of the red and blue circles. Through analysis of intersecting triangles, the ratio is calculated to be 8/9. <br /><br />The document provides detailed solutions using geometric theorems, algebra, and logical reasoning to guide students through these circle-related problems.

Keywords

geometry

circles

Math Kangaroo

radius

Pythagorean theorem

tangent circles

square area

quarter circle arcs

inscribed circles

circle properties