16.1k views
0 votes
Segments in circles maze

Segments in circles maze-example-1
User Moyo
by
4.7k points

1 Answer

6 votes

Answer:

x = 6

Explanation:

You want to know the value of x given a tangent to a circle from an external point has length x, while a secant from that point has length x-2 to the first intersection with the circle, and an additional 5 to the second intersection.

Secant/Tangent relation

The product of the segments of the secant to the two points of intersection with the circle is equal to the square of the tangent segment.

(x -2)(x -2 +5) = (x)² . . . . . use given values

x² +x -6 = x² . . . . . . simplify

x -6 = 0 . . . . . . subtract x²

x = 6 . . . . . . add 6

__

Additional comment

There are rules for two secants, for a tangent and secant (as here), and for two chords internal to the circle. These can be easier to remember if you generalize them to a single rule: the product of the distance from the common point to the first circle intersection and the distance to the second circle intersection is the same for each segment.

For a tangent, the two circle intersections are the same point, hence the distance is squared. For chords, the two circle intersections are at the ends of the chords, and the common point is where the chords cross.

User Karthick
by
5.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.