Construct a right triangle ABC with AB = 6 cm, BC = 8 cm and B = 90°. Draw BD, the perpendicular from B on AC. Draw the circle through B, C and D and construct the tangents from A to this circle.

Steps of construction :

1. Draw a line AB = 6cm

2. Draw ∠ABX = 90°

3. Taking B as center Draw an arc of radius 8 cm which intersects BX at C .

4. Join AC , ABC is the right angled triangle .

5.Now draw BD perpendicular to AC

6. Draw right bisector of BC which intersects BC at M . Taking M as center and BM = MC as center Draw a circle.

7. The draw n circle passes through point B, C and D . [ it follows that angle in a semicircle is right angle]

8. Join AM and draw right bisector of AM which intersects AM at Q

9. Taking Q as center and AQ = QM radius. Draw a circle which intersects the previous circle at B and P

10. Join AB and AP which are required tangents .