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Question

Draw two concentric circles of radii 3 cm and 5 cm. Construct a tangent to smaller circle from a point on the larger circle. Also measure its length.

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Solution

Following are the steps to draw tangents on the given circle:

Step 1

Draw a circle of 3 cm radius with centre O on the given plane.

Step 2

Draw a circle of 5 cm radius, taking O as its centre. Locate a point P on this circle and join OP.

Step 3

Bisect OP. Let M be the midpoint of PO.

Step 4

Taking M as its centre and MO as its radius, draw a circle. Let it intersect the given circle at points Q and R.

Step 5

Join PQ and PR. PQ and PR are the required tangents.

It can be observed that PQ and PR are of length 4 cm each.

In ΔPQO,

Since PQ is a tangent,

∠PQO = 90°

PO = 5 cm

QO = 3 cm

Applying Pythagoras theorem in ΔPQO, we obtain

PQ2 + QO2 = PQ2

PQ2 + (3)2 = (5)2

PQ2 + 9 = 25

PQ2 = 25 − 9

PQ2 = 16

PQ = 4 cm

Hence justified.


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