Question

Determine whether AB is tangent to the circle with center c

Answer 1

9514 1404 393

Answer:

  yes, no, no

Step-by-step explanation:

The triangle will be a right triangle if the sum of the squares of the two short sides, less the square of the long side, is zero. (This is what the Pythagorean theorem tells you.) The angle where the radius meets the circle must be a right angle if the line is to be a tangent.

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a) 3^2 +4^2 -5^2 = 9 + 16 -25 = 0 . . . . AB is a tangent

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b) 9^2 +15^2 -18^2 = 81 +225 -324 = -18 . . . . AB is not a tangent

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c) 10^2 +48^2 -52^2 = 100 +2304 -2704 = -300 . . . . AB is not a tangent