Answer:
(b) 21.4
Step-by-step explanation:
There are a couple of interesting relations regarding chords and secants and tangents of a circle. With the right point of view, they can be viewed as variations of the same relation, possibly making them easier to remember.
When chords cross inside a circle (as here), each divides the other into two parts. The product of the lengths of the two parts of one chord is the same as the product of the lengths of the two parts of the other chord.
Here, that means ...
7x = 10·15
x = 150/7 = 21 3/7 ≈ 21.4
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<em>Additional comment</em>
A secant is a line that intersects a circle in two places. (A tangent is a special case of secant where the two points of intersection are the same point.) When two secants meet outside the circle, there is a special relation between the lengths of the various line segments.
Consider the line segment from the point where the secants meet each other to the far intersection point with the circle. The product of that length and the length to the near intersection point with the circle is the same for both secants.
Here's the viewpoint that merges these two relations:
<em>The product of the lengths from the point of intersection of the lines with each other to the two points of intersection with the circle is the same for each line</em>.
(Note that when the "secant" is a tangent, that product is the square of the distance from the tangent point to the point of intersection with the other line--the distance to the circle multiplied by itself.)
Answer:
C. 75°
Step-by-step explanation:
We have been given a circle and we are asked to find the measure of angle AEC.
We will use Intersecting chords theorem to find the measure of angle AEC, which states that measure of angle formed inside a circle by two intersecting chords is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
We can see that measure of arc AC is 110 degrees and measure of its vertical arc BD is 40 degrees.
Therefore, measure of angle AEC is 75 degrees and option C is the correct choice.
Solve your inequality step-by-step.
7(x+4)>0
Simplify both sides of the inequality.
7x+28>0
Subtract 28 from both sides
.
7x+28−28>0−28
7x>−28
Divide both sides by 7.
7x/7 > −28/7
x > −4
To find this just put 8 over 20 because that is how many red pieces there are divide the equation and you will get 0.4 so I would say the answer is A.
