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Question
Inscribe a regular pentagon in a circle of radius 4 cm. Inscribe a circle in this pentagon and me a sure its radius.
Solution
Steps of construction:
(i) Draw a cir de with centre O and radius = 4 cm.
(ii) Draw radii OT and OP sudi that L TOP = (360/5) = 72°
(iii) Cut off arcs PQ, QR, RS, ST equal to TP.
(iv) Join TP, PQ, QR, RS and ST.
PQRST is the required regular hexagon inscribed in the given circle.
(v) From centre O, drop perpendiculars on TP, PQ, QR, RS and ST at A, B, C, D and E.
(vi) With OA as radius draw a circle touching the five sides of the pentagon.
The circle drawn is the required circle with radius = 3. 3 cm
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