Question 1142858: Find the value of x. Copy and paste link to view image.
https://ibb.co/d2hD552
a. 2
b. 2.5
c. .125
d. 1
My answer is c.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
For future posts, remember that it will always be helpful for us to try to help you if you tell us HOW you got your answer.
Your answer is not correct; but since we don't know how you got it we can't help you see what you did wrong.
Here is the operating principle for this kind of problem.
Each secant intersects the circle in two places. The product of the distances from the external point to the two intersection points is the same for both secants.
So in your problem 1 times 2x must be equal to 1 times 4. That of course means 2x is 4, so x is 2.
Let's look at another more interesting example to help you understand the principle.
Suppose we take the image you provide and change the "1" and "2x" to "2" and "2x" for the upper secant, and change the "1" and "4" for the lower secant to "3" and "9".
Then the distances from the external point to the two intersection points for the lower secant are 3 and 12; the product is 36.
That means the product of "2" and "2+2x" for the upper secant has to be 36 also; that makes 2+2x=18, which leads to x=8.
Answer by ikleyn(52788)  (Show Source):
You can put this solution on YOUR website! .
As I see from the series of your recent posts, there is a gap in your knowledge of properties circles, chords, tangents and secant lines.
In this site, there is a good source to learn it. See the group of lessons
- A circle, its chords, tangent and secant lines - the major definitions
- The longer is the chord the larger its central angle is
- The chords of a circle and the radii perpendicular to the chords
- A tangent line to a circle is perpendicular to the radius drawn to the tangent point
- An inscribed angle in a circle
- Two parallel secants to a circle cut off congruent arcs
- The angle between two chords intersecting inside a circle
- The angle between two secants intersecting outside a circle
- The angle between a chord and a tangent line to a circle
- Tangent segments to a circle from a point outside the circle,
- The converse theorem on inscribed angles
- The parts of chords that intersect inside a circle
- Metric relations for secants intersecting outside a circle (*)
- Metric relations for a tangent and a secant lines released from a point outside a circle
- Quadrilateral inscribed in a circle
- Quadrilateral circumscribed about a circle
As useful addition to the theory, you will find many solved problems for circles, their chords, secant and tangent lines
in the lessons
- Solved problems on a radius and a tangent line to a circle
- Solved problems on inscribed angles
- A property of the angles of a quadrilateral inscribed in a circle
- Solved problems on chords that intersect within a circle
- Solved problems on secants that intersect outside a circle (*)
- Solved problems on a tangent and a secant lines released from a point outside a circle
- The radius of a circle inscribed into a right angled triangle
- Solved problems on tangent lines released from a point outside a circle
The most relevant lessons to your problem are marked (*) in the list.
Also, you have this free of charge online textbook on Geometry
GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.
The referred lessons are the part of this online textbook under the topic "Properties of circles, inscribed angles, chords, secants and tangents ".
Save the link to this online textbook together with its description
Free of charge online textbook in GEOMETRY
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson
to your archive and use it when it is needed.
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