Engineering Board Exam Reviewer · Circles: Chords, Tangents and Secants · hard

Two tangents are drawn from a point P to a circle of radius 6, and the angle between the tangents is 60°. Find the distance from P to the center.

  1. 12
  2. 6.93
  3. 10.39
  4. 18

Answer

A. 12

Solution

The line from P to the center bisects the 60° angle, so 30°=6/OP OP=12.

More Circles: Chords, Tangents and Secants questions

  1. Two circles of radii 8 and 3 touch each other externally. Find the length of their common external tangent.
  2. A chord of length 8 is drawn in a circle of radius 5. Find the height of the circular segment (the sagitta) cut off by the chord.
  3. In a circle of radius 5, two parallel chords of lengths 6 and 8 lie on the same side of the center. Find the distance between them.
  4. A chord 24 cm long lies in a circle of radius 13 cm. Find the distance from the center to the chord, in cm.
  5. From an external point P, a secant meets a circle at A and B with PA=4 and PB=16 (measured from P to each intersection). Find the length…
  6. Chords AB and CD intersect at P inside a circle with AP=6, PB=8 and CP=4. Find PD.
  7. A chord 8 cm long is 3 cm from the center of a circle. Find the radius of the circle in cm.
  8. A point is 13 units from the center of a circle of radius 5. Find the length of the tangent from the point to the circle.
  9. Two chords AB and CD of a circle intersect at a point P inside the circle. If AP=6, PB=8, and CP=4, find PD.
  10. From an external point P, a tangent PT and a secant PAB are drawn to a circle (A nearer to P). If PT=12 and PA=8, find PB.

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