## HelloKitty17 one year ago Geometry Question Layla is using her compass and straightedge to complete a construction of a polygon inscribed in a circle. Which polygon is she in the process of constructing? A circle is drawn with two arc markings above and below the diameter. An equilateral triangle A square A regular pentagon A regular hexagon

1. HelloKitty17

@KAKES1967 @mathmate @thomaster

2. HelloKitty17

3. HelloKitty17

@gigi1103

4. imqwerty

what do u think she will get on joining the points 1 - 2 - 3 -4 :)|dw:1442241380727:dw|

5. HelloKitty17

A regular Hexagon?

6. imqwerty

|dw:1442241736332:dw| how many sides does the figure formed by joining the points 1,2,3,4 has?

7. HelloKitty17

4

8. HelloKitty17

it would be a regular pentagon then!

9. imqwerty

nd u can see that -|dw:1442241878543:dw| in this figure OA =OB=OC=OD=radius of circle =r lets say its r cm ok :) when u apply pythagorus theorem to triangle AOB u get- AO^2 + BO^2 = AB^2 r^2 + r^2=AB^2 2r^2=AB^2 $AB=r \sqrt{2}$ similarly when u find BC, CD and DA you will find that they all are equal to AB :) so this figure has 4 equal sides and square is the only figure given in the options which has 4 sides so square is the answer

10. mathmate