Tangents to Circles Problems

Problem 1 The figure below shows circle A and rectangle ABCD. The measures of segments are indicated. How long is EB? This problem is not that hard. All you need to see is that AB and AE are radius of Circle A. Also, because ABCD is a rectangle, BD = AC. Now, all you need…

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Sum of Consecutive Numbers

Problem 1 Can you work out the answer to this number pattern and explain why you think you have the correct answer? You probably observed that the sum is the square of the middle number. Can you work out why? Why do you have a square number for the sum? Solution 1 Solution 2 Solution…

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Geometric Interpretation of Trapezoid Area Formula

Problem 1 Show that the area of a trapezoid (trapezium) is half its height times the sum of the parallel sides. Solution Cut the trapezoid along the midpoints of the pair of non-parallel side. This halves its height. Rotate one of the parts 180 degrees about a midpoint. In the figure below, it’s about the…

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Proving trigonometric identities #2

Problem: Prove that the equation below is an identity: 2 sin2Ө – sin4Ө = (1 – cos2Ө)(1 + cos2Ө). Solution To prove that an equation is an identity, one must show that the Left Hand Side (LHS) of the equation is identical to its Right Hand Side (RHS). That is, LHS ≡ RHS. Proof LHS: 2 sin2Ө…

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