Mathematics 10 — Exercise 10.2 · Q1

Full question

Draw a tangent at P, the midpoint of arc APB, without using the centre.

Step-by-step solution

  1. Join the endpoints A and B of arc APB.

  2. Construct the perpendicular bisector of chord AB. Because P is the arc midpoint, this bisector passes through P.

  3. At P construct a perpendicular to that bisector and extend it both ways. This is the tangent.

  4. The bisector has the direction of the contact radius, so its perpendicular is tangent.

Answer

The extended line is the required tangent.

APBMCDAB chordperpendicular bisectortangent at PDiagram not to scale