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**Day five:**

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**The inscreibed angle of an intercepted
angle**

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by Nami Youn

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**Objective**

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To discover the relationship of the central angle and the inscribed angle
of an intercepted arc

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To understand the properties of an arc and the inscribed angle of the intercepted
arc

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**1. The relationship of the central
angle and inscribed angle of an intercepted arc**

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**Property 1 : In a circle, the measure
of an inscribed angle is equal to half the measure of the central angle
with the same intercepted arc.**

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**Property 2 : If a triangle is inscribed
in a circle so that one side of the triangle is a diameter of the circle,
then the angle opposite that side is a right angle**

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gsp file

**2. The
properties of an arc and the angle at circumference of an arc**

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**Property 1 : In a circle, the angle
at circumference of the arcs with the same measure are all the same.**

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gsp file

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**Property 2 : In a circle, two inscribed
angles with the same intercepted arc are congruent.**

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**Property 3 : The angle at circumference
of an arc is proportional to the measure of the arc.**

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