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Crystal Catalog Title………………………………………………...1 Catalog…………………………………………….2 Aim and Introduction……………………………….3 Question 1………………………………………………….4 Question 2…………………………………………… 8 Use technology to test …………………………………… Test the validity…………………………………… Discuss the scope………………………………………………13 The final answer and explain the general statement…………. Aim: The aim of this task is to investigate positions of points in intersecting circles. 1 Introduction: The following diagram shows a circle with center and radius r, and any point P. The circle has center and radius. Let A be one of the points of intersection of with. This is show in the diagram below. In order to accomplish this gola, I need to discuss and investegate the 2 dfferent situation of . Used knowledge: 1. The Pythagorass theorem Right side of the hypotenuse is equal to the sum of squared. In this picture 2.cos rule: Rearrangement of the original cosine rule formulae can be used for angle finding if we know all three sides. 3. similar triangle theorem Similar triangles, are the same shape them, but not the same size. But as long as the same shape, no matter how they are size change, so is called similar triangle. If two triangles 3 angle are equal (In fact as long as two angles are equal) we can say these two triangles are similar. 3 Let’s start investigation: In the first condition that is variable and stay the same. When : Draw a graph then link and make a auxiliary line which is a line perpendicular to . is a isosceles triangle. Then because perpendicular to and thus . Assume that . Therefore . and both 4 thus . When: Draw a graph then link and make a auxiliary line which is a line perpendicular to . is a isosceles triangle. Then because perpendicular to and thus . Assume that .Therefore and both