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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

6. Secants, Tangents, and Angle Measures

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Exercise 38 Page 766

Use the Isosceles Triangle Theorem and the Inscribed Angle Theorem.

The arcs have the same measure. See solution.

Practice makes perfect

In the given diagram, we have that △ ABC is an isosceles triangle inscribed in ⊙ D.

Isosceles triangle inscribed in a circle

Since △ ABC is isosceles, we have that AB≅ BC. Then, by the Isosceles Triangle Theorem we also have that ∠ A ≅ ∠ C.

Isosceles triangle inscribed in a circle

Next, thanks to the Inscribed Angle Theorem we get that the measure of each inscribed angle is half the measure of its corresponding intercepted arc.

Isosceles triangle inscribed in a circle and two arcs marked

Finally, since ∠ A ≅ ∠ C, they have the same measure. This implies that the arcs AB and BC have the same measure as well. m ∠ A = m ∠ C ⇒ 1/2m AB &= 1/2m BC ⇒ m AB &= m BC

Subchapter links

Exercises p.763-767