question_answer

Given below are the steps of construction of two tangents to the circle (without using the centre of the circle) of radius 4 cm from point P. Which of the following steps is INCORRECT? Steps of Construction

Step I: Draw a circle of radius 4 cm and take a point P outside the circle and draw a secant PAB, intersecting the circle at A and B.

Step II: Produce AP to C such that\[AP=CP\]. Draw a semicircle with CB as diameter.

Step III: Draw PD 1 CB, intersecting the semicircle at D. With P as centre and PC as radius draw arcs to intersect the given circle at T and T.

Step IV: Join PT and PT. Then, PT and PT are the required tangents.

A)  Only Step I

B)  Both Step I and Step II

C)  Only Step III

D)  Both Step II and Step IV

Correct Answer: C

Solution :

Steps of Construction    Step I: Draw a circle of radius 4 cm and take a point P outside it. Through P draw a secant PAB to intersect the circle at A and B.               Step II: Produce AP to a point C such that\[AP=CP\]. Draw a semicircle with CB as diameter. Step III: Draw \[PD\bot CB\]intersecting the semicircle at D. With P as centre and PD as radius draw arcs to intersect the circle at 7" and T'. Step IV: Join PT and PT. Then, PT and PT are the required tangents.