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larisa [96]
3 years ago
7

Find the length of the missing side. Give your answer in the simplest radical form.

Mathematics
1 answer:
taurus [48]3 years ago
6 0

Answer:

x = 2\sqrt{5}

Step-by-step explanation:

Use Pythagorean theorem,

Hypotenuse² = base² + altitude²

x² = (√8)² + 4²

  =  8 + 16

  = 20

x = √20 = \sqrt{2*2*5} = 2\sqrt{5}

x = 2\sqrt{5}

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<u>Given</u>:

The line segments are AB, DB, AB, OB and BC

We need to determine the given line segments are radius, chord, diameter, secant or tangent of circle O.

<u>Line segment AB:</u>

A secant is a line segment that intersects the circle at two points.

Thus, the line segment AB is a secant.

<u>Line segment DB (</u>\overline{D B}<u>):</u>

The diameter of the circle is line that passes through the center and touches the two ends of the circle.

Thus, from the figure, the line segment DB passes through the center and touches the two ends of the circle.

Hence, the line segment DB is the diameter.

<u>Line segment AB (</u>\overline{A B}<u>):</u>

The line joining any two points on the circle is called the chord of the circle.

Thus, from the figure, the line segment AB touches the two points on the circle.

Hence, the line segment \overline{A B} is the chord of the circle.

<u>Line segment OB (</u>\overline{O B}<u>):</u>

The radius of the circle is any line from the center of the circle to any point on the circle.

Thus, from the figure, the line segment OB is a line from center of the circle to the point B on the circle.

Hence, the line segment \overline{OB} is the radius of the circle.

<u>Line segment BC:</u>

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Thus, from the figure, the line segment BC is a touches the circle exactly once.

Hence, the line segment BC is the tangent of the circle.

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Read 2 more answers
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