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Schach [20]
3 years ago
15

9. The radius of a circle is 6.

Mathematics
1 answer:
Arlecino [84]3 years ago
7 0

Answer:

12,5.196

Step-by-step explanation:

given that the radius of a circle is 6.

We have any tangent drawn from outside point there will be two tangents of equal length and also the line joining point of intersection of tangent with centre of circle will bisect the angle between the tangents.

When angle between the two tangents is 60, we have the right triangle formed by radius, one tangent, and line joining point of intersection of tangent with centre of circle with angles 30,60 and 90

Hence the hypotenuse = length of line segment of tangent = 2 (radius) = 12

Part 2:

When angle between tangents is 120, we have 60,30,90 right triangle and hence length of tangent = radius * sin 60

= 6*\frac{\sqrt{3} }{2} \\=5.196

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3 years ago
one angle of a linear pair is 10 more than two thirds the other angle. find the measure if both angles
BigorU [14]

Answer:

One Angle = 110°

Other Angle = 70°

Step-by-step explanation:

A linear pair means that two angles are in a straight line (or, a straight angle).

A straight line is 180 degrees.

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We can say one angle is "a" and another one is "b".

<em>One angle is 10 MORE THAN 2/3rds of the other, we can write:</em>

<em>a=\frac{2}{3}b+10</em>

<em />

<em>Also, since they are supplementary (add up to 180), we can write:</em>

<em>a + b = 180</em>

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We can now substitute 1st equation in this one and find b:

a+b=180\\(\frac{2}{3}b+10)+b=180\\\frac{2}{3}b+b=180-10\\\frac{5}{3}b=170\\b=\frac{170}{\frac{5}{3}}\\b=170*\frac{3}{5}\\b=110

Since a + b = 180, we can write:

a + 110 = 180

so,

a = 180 - 110

a = 70

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One Angle = 110°

Other Angle = 70°

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