Pearl Angelie Villanueva Mahusay

Student’s Name Professor’s Name Subject DD MM YYYY Geometry Tasks 1. The figure shows two circles. A is the center of the first circle; B is the center of the second circle. What is the measure of angle CBD? The problem states that we have to find the size of CBD. The way it has been redrawn, we should see by symmetry that CBD = 2ϴ. To solve for ϴ, we notice that A is a point on the circumference of circle B. This means that AB is the radius of circle B. Since all radii of a circle are the same (Srivastav 70), the radius from AB = BC = BD. This means that CBA is an equilateral triangle. The size of the angles in an equilateral triangle are all 60°, so that means ϴ = 60°. By symmetry, CBD = 2ϴ = 2 (60°) = 120°. 2. The figure shows an isosceles right triangle ABC. The length of AC is a. Find the length of AB. For this isosceles triangle ABC, AB = BC. Using the Pythagorean Theorem, AB2 + BC2 = AC2, but AC = a. Thus, AB2 + AB2 = a2; then, 2AB2 = a. Simplifying, the answer is AB = a/√2. Furthermore, an isosceles right angle triangle is one of the special triangles whose sides are in the ratio of 1:1. The value of a2 = 12 + 12; a = √2, therefore, the length of AB is 1. 3. The figure shows a circle inscribed in triangle ABC. The circle is tangent to the triangle at point D which divides the side of the triangle into two parts. The length of BD is n, the length of DC is m (m>n). Find the length of AC. After redrawing the figure, it is clearly shown that the radius = n. The red length on the vertical edge will then be given as AB – n; similarly, the blue length on the horizontal edge is given by BC – n or m. Using the property that tangential distances are equal (Srivastav 72), we get AC = AB – n + m Works Cited Srivastav, Manoj Kumar. “Circumcircle and Incircle of A Triangle with Its Impact in Development of Skill.” International Journal of Mathematical Archive, vol. 6, no. 6, 2015, pp. 69-75.