Mathematics 10 — Exercise 10.2 · Q7

Full question

Construct a tangent at any point of a circular track of radius 2 cm.

Step-by-step solution

1. Draw the circle using the specified centre O and radius. Mark the contact point P on its circumference.

2. Join O to P and extend OP through P.

3. Mark equal distances on both sides of P along this line. With those two marks as centres draw equal intersecting arcs. Join their intersection to P.

4. Extend that perpendicular in both directions; call it APB. It makes 90° with OP and is the required tangent.

5. Check with a set square that OP is perpendicular to APB and the line touches the circle only at P.

Answer

The construction above gives the required circle or tangent.