Draw-a-line-segment-equal-to-ab-units-when-AB-a-units-and-CD-b-units-are-given-Only-ruler-and-compass-may-be-used-

Question Number 3647 by Rasheed Soomro last updated on 17/Dec/15

D r a w a l i n e s e g m e n t e q u a l t o

a b u n i t s w h e n A B = a u n i t s a n d C D = b u n i t s

a r e g i v e n . O n l y r u l e r a n d c o m p a s s m a y b e

u s e d .

Commented by prakash jain last updated on 17/Dec/15

Draw a circle of radius CD with center C .

Draw a line ∥ to AB passing thru C . Let

us say it cuts the circle at E .

CE = CD = radius = b

CE ∥ AB

draw ⊥^{r} to AB at B of unit length (BF = 1)

connect AF . △ AFB is right angle triangle

with ∠ B = 90 ° .

\tan ∠ AFB = \frac{AB}{BF} = a

Draw a line l ∥ to AF passing thru C .

Draw a line ⊥^{r} at CE at E .

Let us sat it cut l at G .

△ GCE, ∠ GEC = 90 °,

AF ∥ GC, AB ∥ CE

∠ AFB = ∠ CGE

\tan ∠ CGE = \frac{GE}{CE} = a \Rightarrow GE = a b

Same construction as used in computing

square . unit length is assumed .

Commented by Rasheed Soomro last updated on 19/Dec/15

T h α n k S!

F i r s t I w i l l t r y m y o w n t h e n I w i l l r e a d

y o u r a n s w e r (i n o r d e r t o t r a i n m y s e l f) .