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9.6�Corollaries of TET and its Converse

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Review: TET

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Review: Converse TET

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The Twin Tangent Theorem

Tangents from a point to a circle are equal in length.

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D is a point outside circle A. B and C are points of tangency.

Prove that DB = DC.

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A Corollary of a Corollary

AC and BD below are common external tangent segments; that is, all of A, B, C and D are points of tangency. Prove that AC = BD. (On the problem set, we’ll discover that we have two cases to consider.)

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Circumscribed Polygon Defined

If each of a polygon’s sides is tangent to a circle, then that polygon is circumscribed about the circle.

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BCDE is circumscribed about circle A.

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The Circumscribed Quadrilateral Theorem

If a quadrilateral is circumscribed about a circle, then the sums of its opposite sides are equal.

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BCDE is circumscribed about circle A. Prove that BC + DE = BE + CD.