# CBSE Class 10-Mathematics: Chapter – 11 Constructions Part 16 (For CBSE, ICSE, IAS, NET, NRA 2023)

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Question 28:

Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.

To construct: A circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.

Steps of Construction:

(a) Draw a circle with the help of a bangle.

(b) Take two non-parallel chords AB and CD of this circle.

(c) Draw the perpendicular bisectors of AB and CD. Let these intersect at O. Then O is the center of the circle draw.

(d) Take a point P outside the circle.

(e) Join PO and bisect it. Let be the mid-point of PO.

(f) Taking M as center and MO as radius, draw a circle. Let it intersects the given circle at the points Q and R.

(g) Join PQ and PR.

Then PQ and PR are the required two tangents.

Justification: Join OQ and OR.

Then, is an angle in the semicircle.

Since OQ is a radius of the given circle, PQ has to be a tangent to the circle. Similarly, PR is also a tangent to the circle.