Question

Find the correct order of steps to construct a tangent from an external point P to a circle (where O is the centre of the circle and P is the point from which tangents are drawn).

(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 as LO.

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

Answer 1

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


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. Construct the perpendicular bisector of OP, and name the point of intersection '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.