Page 2: Advanced Circle and Triangle Problems

This page continues with more complex geometry problems from the 2010 and 2011 matura exams.

Circle Equation Problem

The first problem on this page is a continuation from the previous page, asking to find the equation of a circle with center S(4,-2) passing through O(0,0).

Example: The solution involves using the distance formula to find the radius: r² = (0-4)² + (0+2)² = 20. Therefore, the equation is (x-4)² + (y+2)² = 20.

Right Triangle Proof

The next problem requires proving that a triangle with given vertices is a right triangle.

Highlight: This can be solved using the converse of the Pythagorean theorem: if a²+b²=c² for the sides of a triangle, then it is a right triangle.

Circle Tangent Line

Another problem asks to identify the equation of a line tangent to a given circle.

Vocabulary: A tangent line touches the circle at exactly one point.