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.

(ii), (i), (iii), (iv)

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(i), (ii), (iii), (iv)

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(i), (ii), (iv), (iii)

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(ii), (i), (iv), (iiii)

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Solution

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.

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Q. 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.

Given are the steps to construct tangents from an external point P to a circle with centre O. Order the steps correctly.
STEPS:
i) Join PM and PN.

ii) Draw a circle with centre as L and radius LO. Let it cut the given circle at points M and N.

iii) Bisect the segment OP, at L.

iv) Join OP.

To construct the tangents from a point 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 in the first list named as “Steps” and the reasons behind those construction in the next list named “Reasons”. Match them accordingly.

STEPS:
i)Join OP.
ii) Bisect the segment OP, at L.
iii) Draw a circle with centre as L and
radius LO.

iv) From P, join wherever this circle intersects the original circle.

REASONS:
a) Because angle in a semicircle is $90^{\circ}$ and radius is perpendicular to tangent.
b) We get the point(s) of contact, if they exist.
c) To check where the point P lies and hence determining if tangents exist or not.
d) We need to draw a circle with diameter as the distance between the centre of the circle and the point from where tangents should be drawn.

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