Construct-a-line-segment-of-a-2-units-using-ruler-and-compass-only-when-a-line-segment-of-a-units-is-given-

Question Number 3607 by Rasheed Soomro last updated on 16/Dec/15

C o n s t r u c t a l i n e s e g m e n t o f \boldsymbol a^{2} u n i t s

u s i n g r u l e r a n d c o m p a s s o n l y, w h e n

a l i n e s e g m e n t o f \boldsymbol a u n i t s i s g i v e n .

Answered by prakash jain last updated on 16/Dec/15

Let us say line segment is AB .

Draw a (BC) ⊥^{r} to AB at B of length 1 unit let

us point is C .

ABC is right angled triangle with ∠ B = 90 °

\tan C = \frac{AB}{BC} = a

At point B draw a circle of radius AB .

Extend BC let us it cuts the circle at D .

BD = a .

Draw a line l parallel to line AC passing thru

B .

Draw ⊥^{r} to line BD at D . let us say

it cuts line l at E .

Since l (BE) ∥ to line AC and CBD is a straight

line .

∠ A C B = ∠ E B D = x

\tan x = a = \frac{AB}{BC} = \frac{DE}{BD}

BD = a \Rightarrow DE = a^{2}

Commented by Rasheed Soomro last updated on 16/Dec/15

e XCEL l e n t S i r!

\boldsymbol e XCEL l e n t \boldsymbol S i r!