Mathematics 10 — Exercise 10.1 · Q4

Full question

Draw arc PQR and complete the circle without finding its centre.

Step-by-step solution

  1. On the given arc select A,B,C so that consecutive chords AB and BC are equal. Extend AB beyond B to P and BC beyond C to Q.

  2. Measure the exterior angle CBP between BC and the extension BP. Keep this angle as the angle to copy at each next vertex.

  3. At C copy that angle between CQ and a new ray CD on the same turning side. Set the compass to AB and mark D on the ray with CD=AB.

  4. Extend CD; at D copy the same exterior angle. Mark E so DE=AB. Continue equal-chord, equal-turn steps around the circle.

  5. Draw smooth arcs through the successive points to complete the circumference, joining back to the supplied arc. Do not introduce a centre.

  6. Check every new chord against AB and each copied exterior angle against CBP.

Answer

The construction above gives the required circle or tangent.

ABCDEAB=BC=CD=DE=EADiagram not to scale