A horizontal line is the locus of points which have the same displacement to the x-axis. Thus the y-value must not change. Therefore the equation of such a line is:

From the diameter you know that the radius is 10'' long. Draw a rough sketch of the situation. You can see a right triangle with the radius as hypotenuse and the displacement of the chord to the centre as one leg. Use Pythagorean theorem to calculate the missing leg. That would be half of the chord. The complete chord is 16'' long.

...

Use the properties of reflection over an axis. If P is the original point and P' is the image of P then PP' perpendicular to the y-axis and the y-axis bisect the distance PP'. Thus P'(3, -5)

Use the property: angle + compliment = 180°.

With your problem the angle = 5 * compliment. Therefore:

5*compliment + compliment = 180°

6* compliment = 180°

compliment = 30°

thus angle = 5*compliment = 150°

From 2x + y = 7 ==> y = -2x + 7.

Therefore the slope of the given line is m = -2. A perpendicular line has the slope m' = ½

Now use point-slope formula to get the equation of the line:

Because the angle at C must be a right angle. Therefore you are dealing with a right triangle.

An octagon consists of 8 congruent sosceles triangles. If s is the side of the octagon, the half diameter of the octagon is r, the apothem is a and the angle at the centre of the octagon is then you can use some trigonometric formulae:

Plug in the values you know:

I don't know which method you use to solve such a system....

3x+2y=17

2x-y=9 multiply this equation by 2

3x+2y=17

4x-2y=18 add columnwise(?)

7x = 35 divide by 7

x = 5 substitute 5 instead of x in the 2nd equation:

10 - y = 9 ==> y = 1