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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Find an equation for the perpendicular bisector of the line segment whose endpoints

TEA [102]

Answer:

y= -2x -8

Step-by-step explanation:

I will be writing the equation of the perpendicular bisector in the slope-intercept form which is y=mx +c, where m is the gradient and c is the y-intercept.

A perpendicular bisector is a line that cuts through the other line perpendicularly (at 90°) and into 2 equal parts (and thus passes through the midpoint of the line).

Let's find the gradient of the given line.

$\boxed{gradient = \frac{y1 -y 2}{x1 - x2} }$

Gradient of given line

$= \frac{1 - ( - 5)}{3 - ( - 9)}$

$= \frac{1 + 5}{3 + 9}$

$= \frac{6}{12}$

$= \frac{1}{2}$

The product of the gradients of 2 perpendicular lines is -1.

(½)(gradient of perpendicular bisector)= -1

Gradient of perpendicular bisector

= -1 ÷(½)

= -1(2)

= -2

Substitute m= -2 into the equation:

y= -2x +c

To find the value of c, we need to substitute a pair of coordinates that the line passes through into the equation. Since the perpendicular bisector passes through the midpoint of the given line, let's find the coordinates of the midpoint.

$\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2}) }$