question_answer

Let ABC be a right triangle in which \[AB=3\text{ }cm,\text{ B}C=4\text{ }cm\]and \[\angle B={{90}^{o}}\]. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Given below are the steps of constructions of a pair of tangents from A to this circle. Which of the following steps is INCORRECT?   Steps of Construction

Step I: Draw \[\Delta ABC\] 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 diameter. This circle cuts the circle drawn in step II at S and P. Join /AO, AP and AB are desired tangents drawn from A to the circle passing through B, C and D.

A)  Only Step I                 

B)  Only Step II                

C)  Only Step III    

D)  Only Step IV