Geometry FLVS 07.02 Inscribed and Circumscribed Circles

Point D is the incenter of triangle BCA. If m∠FHG = 61°, what is the measure of ∠FDG?

122°

The vertices of triangle HIJ lie on circle K, as shown. If m∠IHJ is 72°, what is m∠IJH?

18°

A company is replacing cables with fiber optic lines in rectangular casing BCDE. If DE = 2.5 cm and BE = 3 cm, what is the smallest diameter of pipe that will fit the fiber optic line? Round your answer to the nearest hundredth.

3.91 cm

Quadrilateral CDEF is inscribed in circle A. If m∠CFE = (2x + 6)° and m∠CDE = (2x − 2)°, what is the value of x?

44

This is a cross-sectional view of candy bar ABC. A candy company wants to create a cylindrical container for candy bar ABC so that it is circumscribed about the candy bar. If = 2.5 cm, what is the smallest diameter of wrapper that will fit the candy bar?

5 cm

This is a cross-sectional view of candy bar ABC. A candy company wants to create a cylindrical container for candy bar ABC so that it is circumscribed about the candy bar. If = 3 cm, what is the smallest diameter of wrapper that will fit the candy bar?

6 cm

Point D is the incenter of triangle BCA. If m∠FDG = 128°, what is the measure of ∠FHG?

64°

Quadrilateral CDEF is inscribed in circle A. If m∠C = 9x° and m∠E = 7x + 4°, what is the measure of ∠E?

81°

Quadrilateral CDEF is inscribed in circle A. If m∠C = 7x + 11° and m∠E = 7x + 1°, what is the measure of ∠E?

85°

Noah is baking a two-layer cake, in which the bottom layer is a circle and the top layer is a triangle. If AB = 5 inches and Arc AB ≅ Arc AC, what does Noah know about the top layer of his cake?

AB ≅ AC because their arcs are congruent; therefore, ΔABC is an isosceles triangle.

What is the first step in constructing a circumscribed circle around triangle XYZ?

Construct the perpendicular bisector of segment XY.

Triangle Town wants to build a school that is equidistant from its three cities, L, M, and N. Which construction correctly finds the best location of the school?

Construction Y, because point E is the circumcenter of ΔLMN

James is constructing a circle circumscribed about a triangle. He has partially completed the construction, as shown below. What should be his next step in the construction?

Use the circumcenter to determine the center of the circle.

Aaron is constructing a circle circumscribed about a triangle. He has partially completed the construction, as shown below. What should be his next step in the construction?

Use the compass to find the perpendicular bisector for side DF.