Question

Can someone solve this?

Answer 1

Answer:

• x = 6
• y = 18

Step-by-step explanation:

The relevant relation is that the product of distances from the point of intersection of secants to the two points of intersection of each with the circle is a constant. The point of tangency counts as both points of intersection.

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By way of example, the product of distances to the circle for the tangent segment is 10·10 = 100

This is also the product of the distances on the secant that intersects the tangent:

  100 = 5(5+x+9)

  20 = x +14 . . . . . divide by 5

  x = 6 . . . . . . . . . . subtract 14

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The same is true when the secants intersect inside the circle:

  6·9 = y·3

  y = 18 . . . . . . divide by 3