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Apply geometry across unfamiliar problems

Apply geometry across unfamiliar problems: original cases with explanations after your first response.

Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.

1. What you will learn

Mark only stated equalities, right angles and parallel lines. Select the relationship that connects the given dimensions to the requested angle, length or area.

2. Practice

Two angles of a triangle measure 37 and 58 degrees. How many degrees is the exterior angle at the third vertex?

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3. Practice

A regular polygon has exterior angles of 24 degrees. How many sides does it have?

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4. Practice

A right triangle has legs 9 and 12. What is the radius of the circle with its hypotenuse as diameter?

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5. Practice

A circle of radius 6 has a sector with central angle 120 degrees. What is the sector's area divided by pi?

Answer:

6. Practice

A chord is 16 units long in a circle of radius 10. What is the perpendicular distance from the center to the chord?

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7. Practice

A tangent from point P touches a circle at T. The center O satisfies OP=13 and OT=5. What is PT?

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8. Practice

Two sides of a triangle have lengths 4 and 9. How many positive integer lengths are possible for the third side?

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9. Practice

A square is inscribed in a circle of radius 5. What is the square's area?

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10. Practice

A circle's circumference is 18 pi. What is its area divided by pi?

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11. Practice

Two concentric circles bound a ring. Their radii differ by 3 and their circumferences sum to 30 pi. What is the ring's area divided by pi?

Answer:

12. What you can do now

Check whether a squared scale factor is needed, and distinguish a radius from a diameter before interpreting the final measure.