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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.
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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