   Chapter 6.3, Problem 50E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

The sides of ∠ A B C are tangent to ⊙ D at A and C, respectively. Explain why quadrilateral ABCD must be a kite. To determine

To explain:

Why quadrilateral ABCD must be a kite.

Explanation

Given that the sides of ABC are tangent to D at A and C, respectively.

To prove quadrilateral ABCD must be a kite.

The diagrammatic representation is given below,

Theorem:

The tangent segments to a circle from an external point are congruent.

Then AB¯andAC¯ are tangents to O from point A; B and C are points of tangency.

Therefore, AB¯AC¯

Also DA and DC are equal since DA and DC are radius of the circle (radius is same for all points on the circle)

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