Geometry | Unit 7 | Lesson 5: Triangles in Circles | Practice Problems

Do you agree with either of them? Explain or show your reasoning.

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The distance between points \(E\) and \(B\)? Explain or show your reasoning.

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Construct the circumcenter of each triangle. Then, based on the locations of the circumcenters, classify each triangle as acute, right, or obtuse.

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Select all quadrilaterals that cannot be cyclic.

• a square with side length \(\sqrt5\) units

• a 2 inch by 4 inch rectangle

• a rhombus with side length 5 centimeters and angle measures 20 degrees and 160 degrees

• quadrilateral \(ABCD\) in which angle \(A\) is 62 degrees, angle \(B\) is 97 degrees, angle \(C\) is 118 degrees, and angle \(D\) is 83 degrees

• quadrilateral \(WXYZ\) in which angle \(W\) is 45 degrees, angle \(X\) is 135 degrees, angle \(Y\) is 90 degrees, and angle \(Z\) is 90 degrees

A quadrilateral \(ABCD\) has the given angle measures. Select the set of measurements which could come from a cyclic quadrilateral.

• angle \(A\) is 70\(^\circ\), angle \(B\) is 110\(^\circ\), angle \(C\) is 70\(^\circ\), and angle \(D\) is 110\(^\circ\)

• angle \(A\) is 60\(^\circ\), angle \(B\) is 50\(^\circ\), angle \(C\) is 120\(^\circ\), and angle \(D\) is 130\(^\circ\)

• angle \(A\) is 100\(^\circ\), angle \(B\) is 110\(^\circ\), angle \(C\) is 70\(^\circ\), and angle \(D\) is 80\(^\circ\)

• angle \(A\) is 70\(^\circ\), angle \(B\) is 45\(^\circ\), angle \(C\) is 110\(^\circ\), and angle \(D\) is 45\(^\circ\)

What is the measure of angle \(YXZ\)?

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What is the measure of angle \(ACB\)?

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What is the measure of the arc from \(A\) to \(B\) not passing through \(C\)?

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A quadrilateral has vertices \(A=(0,0), B=(2,4), C=(0,5),\) and \(D=(\text-2,1)\). Select the most precise classification for quadrilateral \(ABCD\).

• quadrilateral

• parallelogram

• rectangle

• square