The Proof of the Second Case of the Inscribed Angle Theorem

In December last year, we have proved one case of the Inscribed Angle Theorem. In this post, we prove the second case. Note that the order of the cases does not matter; we just placed ordinal numbers to distinguish one from the other. Recall that the first case of the theorem involved drawing an auxiliary […]
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Triangles with Non Congruent Sides

We have shown that in an isosceles triangle, the angles opposite the congruent sides are congruent. This was the Isosceles Triangle Theorem which we proved two weeks ago. In this post, we are gong to learn a slightly related theorem: a theorem that states that if in a triangle, two sides are not congruent, then […]
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The Angle Secant Theorem

A secant is a line that intersects a circle at two points. In the figure below, is formed by two secants. The angle intercepts two arcs and . In this post, we will prove that the measure of the angle formed by two secants intersecting outside a circle is half the difference of the arcs […]
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