Circles

SAT Math· difficulty 5/5

A triangle is inscribed in a circle of radius 10. One inscribed angle measures 45°45°. What is the length of the chord opposite this angle?

  • A

    10

  • B

    10210\sqrt{2}

    check_circle
  • C

    525\sqrt{2}

  • D

    20

Explanation

The chord opposite a 45°45° inscribed angle subtends a 90°90° arc. The chord, two radii, form a 45-45-90 triangle... actually a right triangle with legs = radii = 10. Chord = sqrt102+102=10sqrt2\\sqrt{10^2 + 10^2} = 10\\sqrt{2}.

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