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Question

Explain the steps to construct tangents to a circle from a point P outside the circle and prove that they are tangents to the circle.


Solution

The steps for construction of a tangent from a point outside the circle are:

a)      Draw a line segment from P to the centre of the circle O and bisect it. Let the bisection is done at a point, say M.

b)      With PM as radius draw a circle. Let this circle intersect the initial circle at points X and Y

c)       Join PX and PY. They are the required tangents.

Since PO is the diameter of the new circle, X and  Y are 90( Angles in a semicircle)

But OX and OY are radii of the circle.

Any line that makes a right angle with a radius and touches the circle at only 1 point is a tangent to a circle.

Hence PX and PY should be tangents to the circle.


Mathematics

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