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Question
Construct the rhombus ABCD whose diagonals AC and BD are of lengths 8 cm and 6 cm respectively. Construct the inscribed circle of the rhombus. Measure its radius.
Solution
Steps of construction:
1) Draw AC = 8 cm
2) Draw perpendicular bisector of AC = cut it at I.
3) Cut IB = `6/2` = 3cm and ID = 3 cm and join ABCD. Then ABCD is the required rhombus.
4) Now form I draw a perpendicular to BC to meet it at L.
5) With I as centre and IL as radius draw a circle which is the required circle. Its radius = IL = 2.4 cm.
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RELATED QUESTIONS
Using ruler and compass construct a cyclic quadrilateral ABCD in which AC = 4 cm, ∠ ABC = 60°, AB 1.5 cm and AD = 2 cm. Also, write the steps of construction.
(a) Only the ruler and compass may be used in this question. All contraction lines and arcs must be clearly shown and be of sufficient length and clarity to permit assessment.
(i) Construct a ABC, such that AB = AC = 7 cm and BC = 5 cm.
(ii) Construct AD, the perpendicular bisector of BC.
(iii) Draw a circle with center A and radius 3 cm. Let this circle cut AD at P.
(iv) Construct another circle, to touch the circle with center A, externally at P, and pass through B and C.
