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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
DOnly V

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

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