Question

Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and ∠B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.

Answer 1

Steps of Construction :

• Construct ∆ABC such that BC = 8 cm, AB = 6 cm and ∠ABC = 90°.
• Draw BD ⊥ AC.
• ∠CDB = 90° So, BC is the diameter of circle passing through B, C, D
• Bisect line BC at O.
• O as the centre, CO = OB as radius draw a circle which passes through B, C, D.

• Join AO which intersects the circle at M.
• M as centre and MA = OM as radius draw another circle which intersect the previous circle at P and B.
• Join PA.
  Then, AP and AB are the required tangents.

Justification :

∠ABC = 90° [By Construction]

AB ⊥ OB.

OB is radius and AB is tangent. Similarly, AP is tangent.