Question

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Tangent Property



Solve the following problems. Remember that all reasoning must be explained, and all steps of math work must be shown!

Answer 1

Answer:

see below

Step-by-step explanation:

1) Length of side OQ can be solved by using Pythagorean

OQ² = 3² + 4²

        = √25

        = 5

2)  Length of side PQ can be solved by using Pythagorean

13² = 5² + PQ²

PQ² = 13² - 5²

       = √144

       = 12

3) Length of side RS and SQ can be solved by using Pythagorean

RS² = 13² - 6²

       = √133

       = 11.5

SQ² = 8² - 6²      

       = √28

       = 5.3

Answer 2

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Answer:

1. OQ = 5.0
2. PQ = 12.0
3. RS = 11.5, SQ = 5.3

Step-by-step explanation:

A tangent meets the radius at right angles at the point of tangency. The triangles here are all right triangles, so the Pythagorean theorem can be used to find the missing side lengths.

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1. a² = 3² +4² = 25

  a = √25 = 5 = OQ

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2. 5² +a² = 13²

  a² = 13² -5² = 144

  a = √144 = 12 = PQ

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3. a = √(13² -6²) = √133 ≈ 11.5 = RS

  b = √(8² -6²) = √28 ≈ 5.3 = SQ