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

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 of the tangent from P.

  1. 10
  2. 12
  3. 6.93
  4. 8

Answer

D. 8

Solution

Tangent-secant theorem: t2=PA· PB=4(16)=64 t=8.

More Circles: Chords, Tangents and Secants questions

  1. Chords AB and CD intersect at P inside a circle with AP=6, PB=8 and CP=4. Find PD.
  2. A chord 8 cm long is 3 cm from the center of a circle. Find the radius of the circle in cm.
  3. 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.
  4. 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.
  5. 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.
  6. Two secants from an external point P intersect a circle: one at A and B (with PA=5, AB=7), the other at C and D (with PC=6). Find PD.
  7. A tangent segment from an external point to a circle measures 15 cm, and the distance from the external point to the center is 17 cm. Find…
  8. Find the length of a tangent drawn from a point 13 cm from the center of a circle with radius 5 cm.
  9. Two circles are tangent externally. Their radii are 4 cm and 9 cm. Find the distance between their centers.
  10. Two circles with radii 5 and 12 have centers 13 units apart. Find the length of their common chord.

All Circles: Chords, Tangents and Secants questions