Question

To construct a tangent from a point P to a circle (where O is the centre of the circle and P is the point from which tangents are drawn). Following are the steps of construction but they are not in order. Find the correct order of these steps.

(i) Bisect the segment OP, at L.
(ii) Join OP.
(iii) From P, join wherever this circle intersects the original circle.
(iv) Draw a circle with centre as L and radius LO.

• A. (ii), (i), (iii), (iv)
• B. (i), (ii), (iii), (iv)
• C. (i), (ii), (iv), (iii)
• D. (ii), (i), (iv), (iiii)

Answer 1

The correct option is D (ii), (i), (iv), (iiii)


Step 1: Join PO. By joining OP, we are determining the location of P because if P is less than radius OM then we cannot have a tangent from point P.
Step 2: Bisect the segment OP, at L. Find the bisector of the line OP and name it as L.
Step 3: Draw a circle with centre as L and radius LO. This is to find the point of contact of the required tangent. Name that point as M.
Step 4: From P, join wherever this circle intersects the original circle. Join MP. Now, MP is the required tangent from point P to the circle with centre O.

Similarly, Join P and the other point where the circle with center L and radius OL intersects the circle with center O and radius OM, to get the other tangent.