Mathematics 10 — Exercise 10.2 · Q8

Full question

A machine wheel has radius 2.1 cm. Construct two tangents from a pulley point meeting at 30°.

Step-by-step solution

  1. Draw the circle of the given radius and a diameter AOB.

  2. At B construct a perpendicular to OB; this gives the first tangent.

  3. At O construct angle AOC=30°: first construct 60° with an equilateral triangle, then bisect it with equal arcs. Let ray OC meet the circumference at C.

  4. At C construct the perpendicular to OC. Extend it to meet the first tangent at P.

  5. Since AOB=180°, BOC=180°−30°=150°. The two contact angles are 90°. In quadrilateral BOCP, BPC=360°−90°−90°−150°=30°.

  6. Thus PB and PC are the required tangents. Verify their equal lengths and the 30° meeting angle.

Answer

The construction above gives the required circle or tangent.

OABCPr=2.1 cm∠AOC=30°∠BPC=30°Diagram not to scale