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Point P lies on circle C, x^2+y^2=36. There are two unique tangents to circle D, x^2+y^2=18 that pass through point p. What is the measure of the angle between the two tangent lines?

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mhanifa

Answer:

  • 90°

Step-by-step explanation:

Refer to attached

Red circle is C with radius 6 and green circle is D with radius √18.

PM and PN are tangents to circle D.

M and N are right angles as tangents are perpendicular to radius.

We need to find the measure of ∠MPN.

We'll work out this angle using trigonometry:

  • OM / OP = sin (∠MPO)
  • sin (∠MPO) = √18/6 = √2/2
  • m∠MPO = arcsin ( √2/2) = 45°

∠NPO is same as ∠MPO, therefore:

  • m∠MPN = 45°*2 = 90°
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