Question

Let ABC be a right 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 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 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 diameter. This circle cuts the circle drawn in step II at B and P. AO, AP and AB are desired tangents drawn from A to the circle passing through B, C and D.

(A) Only Step I

(C) Only Step III

(B) Only Step II

(D) Only Step IV

Answer 1

The correct option is: (D) Only Step IV

Explanation:

Only AB and AP are tangents to the given circle.

AO is secant to the circle.

So, step IV is incorrect.