Exploring Shapes Inscribed in Circles

What is true about the hypotenuse of a right triangle inscribed in a circle?

• It equals the radius of the circle.

• It is perpendicular to the diameter.

• It is less than the radius of the circle.

• It is the diameter of the circle.

If the longest side of a triangle is the diameter of a circle, what type of triangle is it?

• Right triangle

• Equilateral triangle

• Isosceles triangle

• Scalene triangle

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CCSS.HSG.CO.C.9

Given a right triangle inscribed in a circle, if one angle measures 45 degrees, what is the measure of the arc it intercepts?

• 180 degrees

• 135 degrees

• 90 degrees

• 45 degrees

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CCSS.HSG.C.A.2

What is the measure of an angle that intercepts a semicircle?

• 90 degrees

• 135 degrees

• 180 degrees

• 45 degrees

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CCSS.4.MD.C.5B

CCSS.HSG.CO.A.1

In a circle, what is the relationship between opposite angles of an inscribed quadrilateral?

• They are complementary.

• They are supplementary.

• They are equal.

• They are congruent.

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CCSS.HSG.C.A.2

What is the sum of the measures of opposite angles in an inscribed quadrilateral?

• 90 degrees

• 180 degrees

• 360 degrees

• 270 degrees

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CCSS.HSG.C.A.3

How can the measure of an angle in an inscribed quadrilateral be determined?

• By doubling the measure of its intercepted arc

• By halving the measure of its intercepted arc

• By subtracting the measure of its intercepted arc from 360

• By adding 180 to the measure of its intercepted arc

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CCSS.HSG.C.A.2

What must be true for a quadrilateral to be inscribed in a circle?

• Its diagonals must intersect at the center of the circle.

• It must have at least two right angles.

• Its opposite angles must be supplementary.

• All its sides must be equal.

If angle X and angle Y are opposite angles in an inscribed quadrilateral, and angle X is 80 degrees, what is the measure of angle Y?

• 80 degrees

• 90 degrees

• 105 degrees

• 100 degrees

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CCSS.HSG.C.A.2

In an inscribed quadrilateral, if one angle measures 30 degrees, what is the measure of its opposite angle?

• 60 degrees

• 30 degrees

• 150 degrees

• 180 degrees

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CCSS.HSG.C.A.3