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

Step of Construction:

Step 1: Draw BC = 8 cm.

Step 2: From B draw an angle of 90 �.

Step 3: Draw an arc ⌒ BC = 6 cm cutting the angle at A.

Step 4: Join AC. ΔABC is the required .

Step 5: Draw ⊥ bisector of BC cutting BC at M.

Step 6: Take M as centre and BM as radius, draw a circle.

Step 7: Take A as centre and AB as radius draw an arc cutting the circle at E. Join AE.

Step 8: AB and AE are the required tangents.

Justification:

Given: ∠AOB = 90°

Since, OB is a radius of the circle.

∴ AB is a tangent to the circle.

Also, AE is a tangent to the circle.

Ans. The required right-angled triangle and its tangents are drawn.