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प्रश्न
Two straight roads AB and CD cross each other at Pat an angle of 75° . X is a stone on the road AB, 800m from P towards B. BY taking an appropriate scale draw a figure to locate the position of a pole, which is equidistant from P and X, and is also equidistant from the roads.
उत्तर
Steps of construction:
(i) Draw two lines AB and CD crossing at an angle of 75 °
(ii) Draw an angle bisector for ∠ BPD
(iii) Draw perpendicular from X on angle bisector meeting at 0.
(iv) From point Y, PX = PY, draw a perpendicular on angle bisector meeting at 0.
(v) 0 is the point which is equidistant from P, X and both the roads.
cos θ = `"hypotenuse"/"base"`
cos `75/2 = "PO"/"PX"`
cos (37.5) = `"PO"/800`
0.980243 = `"PO"/800`
PO = 784.19 m
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संबंधित प्रश्न
Use ruler and compasses only for this question:
I. Construct ABC, where AB = 3.5 cm, BC = 6 cm and ABC = 60o.
II. Construct the locus of points inside the triangle which are equidistant from BA and BC.
III. Construct the locus of points inside the triangle which are equidistant from B and C.
IV. Mark the point P which is equidistant from AB, BC and also equidistant from B and C. Measure and records the length of PB.
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- Measure and record the length of AB.
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Ruler and compasses only may be used in this question. All construction lines and arcs must be clearly shown, and be of sufficient length and clarity to permit assessment.
(i) Construct a ΔABC, in which BC = 6 cm, AB = 9 cm and ∠ABC = 60°.
(ii) Construct the locus of the vertices of the triangles with BC as base, which are equal in area to ΔABC.
(iii) Mark the point Q, in your construction, which would make ΔQBC equal in area to ΔABC, and isosceles.
(iv) Measure and record the length of CQ.
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