Mathematics 10 — Exercise 10.2 · Q5

Full question

Construct a circle of radius 1.5 cm and a tangent from P, 8 cm from its centre.

Step-by-step solution

  1. Draw the given circle with centre O. Mark external P at the specified distance from O; join OP.

  2. Construct the perpendicular bisector of OP using equal compass arcs. Its intersection with OP is the midpoint M.

  3. With centre M and radius MO draw the auxiliary circle on diameter OP.

  4. Mark its intersections T,U with the original circle. Join PT and PU.

  5. Angles OTP and OUP stand on auxiliary diameter OP, so both are 90°. Therefore PT and PU are the two required tangents.

  6. Check that PT=PU and each line is perpendicular to its contact radius.

Answer

The construction above gives the required circle or tangent.

OTUPr=3/2 cmOP=8 cmDiagram not to scale