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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.
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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
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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
