Question

Find x [Angles and Segment]

Answer 1

Answer:

  8.3 cm

Step-by-step explanation:

The product of lengths to the near and far point of intersection with the circle is the same in all cases:

  (7 cm)(7 cm) = (y)(11 cm +y) = (4 cm)(4 cm +x)

Since we're only interested in x, we can divide by 4 and subtract 4:

  49 cm² = (4 cm)(4 cm +x)

  (49/4) cm = 4 cm +x . . . . . . divide by 4 cm

  8.25 cm = x . . . . . . . . . . . . . subtract 4 cm

To the nearest tenth, x = 8.3 cm.

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For a tangent segment, the two points of intersection with the circle are the same point, so the product of lengths is the square of the length.

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The angles depend on the size of the circle, which is not given.