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gizmo_the_mogwai [7]
2 years ago
6

How do you solve for X and A? ​

Mathematics
1 answer:
Ainat [17]2 years ago
4 0

9514 1404 393

Answer:

  3.  x = 10

  4.  a = 8

Step-by-step explanation:

A reasonably simple rule to remember for secants outside the circle or chords inside the circle: <em>the product of the lengths from the point of intersection of the lines to the points of intersection of the circle is the same for each line</em>.

When the external line is tangent to the circle, the two points of intersection of the line with the circle are the same: the point of tangency. Effectively, this means the length is squared.

__

3. For line QP, the product is 3(3+5) = 24.

For line QR, the product is 2(2+x). The rule above says these are equal:

  24 = 2(2+x)

  12 = 2+x . . . . . divide by 2

  10 = x . . . . . . . subtract 2

__

4. For line BC, the product is (a)(a) = a^2.

For line GC, the product is 4(12+4) = 64. The rule above says these are equal:

  a^2 = 64

  a = √64 . . . . take the square root

  a = 8

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