Subject :IMO Class : Class 10

Let ABC be a right angled triangle in which AB = 3 cm, BC = 4 cm and ∠B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn.

Given below are steps of construction of tangents from A to this circle. Identify the wrong step. Steps of construction :

**Step I :** Draw ΔABC and perpendicular BD from B on AC.

**Step II :** Draw a circle with BC as a diameter. This circle will pass through D.

**Step III :** Let O be the mid point of BC. Join AO.

**Step IV :** Draw a circle with AO as radius. This circle cuts the circle drawn in step II at B and P.

**Step V : **Join AP. AP and AB are desired tangents drawn from A to the circle passing through B, C and D.

AOnly I

BOnly IV

COnly III

DOnly V

AO should be the diameter, and not the radius, hence Step IV is incorrect.