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प्रश्न
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.
उत्तर
Steps of construction:
1) Draw a line segment AC = 4 cm.
2) Draw ∠ CAX = 60°.
3) Draw the perpendicular bisector MN of AC.
4) Draw EA ⊥ AX at point A which intersects MN at O.
5) With Centre O and radius OA draw a circle.
6) Mark a point B on the circumference of the circle such that AB = 1.5 cm and mark a point D on the circumference so that AD = 2.0 cm.
7) Join BC and measure ∠ ABC = 60°. Then ABCD is the required cyclic quadrilateral.
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संबंधित प्रश्न
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.
(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.
