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प्रश्न
Inscribe a regular pentagon in a circle of radius 4 cm. Inscribe a circle in this pentagon and me a sure its radius.
उत्तर
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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संबंधित प्रश्न
Construct a regular hexagon of side 5 cm. Construct a circle circumscribing the hexagon. All traces of construction must be clearly shown.
Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon.
Inscribe a regular hexagon in a circle of radius 3 .5 cm.
Circumscribe a regular pentagon about a circle of radius 3 cm.
Draw a circle of radius 2.5 cm and circumscribe a regular hexagon about it.
Use a ruler and compass only for this question to construct the cyclic quadrilateral ABCD in which AB = 5 cm, BC = 8 cm, ∠ ABC = `67 1/2 °`, and D is equidistant from B and C.
