By geometrical construction is it possible to divide a line segment in ratio (root 3+2):(3-root2) Ans - Maths - Coordinate Geometry

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By geometrical construction is it possible to divide a line segment
in ratio (root 3+2):(3-root2)?? Ans this question only Font give
link to other question where ratio is different!!! Ans of this
ratio ONLY

Neha Sethi · Accepted Answer

Dear student Yes, it is possible to divide a line segment in the ratio $3 + \sqrt{2} : 3 - \sqrt{2}$ by geometrical construction Steps of construction are given below Step 1: Draw a line segment AB Step 2: Draw any ray AD, making an acute angle ∠BAD with AB Step 3: Along AD, mark off point A1, A2, A3, A4, A5, A6 such that AA1 = A1A2 = A2A3 = A3A4 = A4A5 = A5A6 = 1 units Step 4: Join BA6 Step 5: Draw A4C ⊥ AD at A4 such that A4C = 1 unit Step 6 : Join A3C Step 7: With A3 as centre and radius = A3C draw an arc intersecting AD in X Step 8: Draw XY || A6B, intersecting AB in Y

Here, Y divides AB in the ratio $3 + \sqrt{2} : 3 - \sqrt{2}$ Justification: $AX = 3 + \sqrt{2} {XA}_{6} = 6 - AX = 6 - (3 - \sqrt{2}) = 3 - \sqrt{2}$ ΔAXY ∼ ΔABA6 (AA similarity) $∴ \frac{AY}{YB} = \frac{AX}{{XA}_{6}} (Corresponding sides are proportional) \Rightarrow \frac{AY}{BY} = \frac{3 + \sqrt{2}}{3 - \sqrt{2}} \Rightarrow AY : BY = 3 + \sqrt{2} : 3 - \sqrt{2}$ Regards

By geometrical construction is it possible to divide a line segment in ratio (root 3+2):(3-root2)?? . Ans this question only . Font give link to other question where ratio is different!!!. Ans of this ratio ONLY