C Challenge

30. Proof Write an indirect proof of Theorem 12-2.

    Given: A B ¯ ⊥ O P ¯ eh b bar , up tack , o p bar  at P.

    Prove: A B ¯ eh b bar  is tangent to ⊙ O . circle dot o .

    

31. Two circles that have one point in common are tangent circles. Given any triangle, explain how to draw three circles that are centered at each vertex of the triangle and are tangent to each other.

Standardized Test Prep

SAT/ACT

GRIDDED RESPONSE

Lines in ⊙ O circle dot o  that appear to be tangent are tangent. What is the value of x?

32. 
33. 

34. The diagram below shows the dimensions of a silo. What is the volume of the silo to the nearest cubic foot?

    

35. The perimeter of an equilateral triangle is 90 in. What is its area to the nearest square inch?

Mixed Review

See Lesson 11-7.

Two cubes have heights 6 in. and 8 in. Find each ratio.

36. scale factor
37. ratio of surface areas
38. ratio of volumes

See Lesson 8-3.

Algebra Find the value of x. Round answers to the nearest tenth.

Get Ready! To prepare for Lesson 12-2, do Exercises 42–44.

See Lesson 8-2.

Find the value of each variable. Leave your answer in simplest radical form.

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