Thursday, 23 August 2012

Circles

AB & CD are two parallel chords drawn on two opposite sides of their parallel diameters such that AB=6cm,CD= 8cm.if the radius of the circle is 5cm,the distance between the chords,in cm, is
 
A 2     B 8
C 5   D 3

drawing%28200%2C200%2C-5%2C5%2C-5%2C5%2Ccircle%280%2C0%2C5%29%2Cline%28-3%2C4%2C3%2C4%29%2Cline%28-4%2C-3%2C4%2C-3%29%2C%0D%0Alocate%28-3.45%2C4.45%2CA%29%2Clocate%283.2%2C4.45%2CB%29%2C+locate%28-4.2%2C-3%2CC%29%2C+locate%284%2C-3%2CD%29%2C%0D%0Ared%28line%28-5%2C0%2C5%2C0%29%29%2Clocate%280%2C4.75%2C6%29%2C+locate%280%2C-3%2C8%29%2C+locate%28.2%2C.8%2CO%29%2Ccircle%280%2C0%2C.1%29%2C+locate%28-.2%2C0%2C10%29%0D%0A%29
Draw a green diameter perpendicular to the red diameter, which biscects 
chord AB at E into two 3 cm parts, chord CD at F into two 4 cm parts, and the
red diameter into two 5 cm radii 

drawing%28200%2C200%2C-5%2C5%2C-5%2C5%2Ccircle%280%2C0%2C5%29%2Cline%28-3%2C4%2C3%2C4%29%2Cline%28-4%2C-3%2C4%2C-3%29%2C%0D%0Alocate%28-3.45%2C4.45%2CA%29%2Clocate%283.2%2C4.45%2CB%29%2C+locate%28-4.2%2C-3%2CC%29%2C+locate%284%2C-3%2CD%29%2C%0D%0Ared%28line%28-5%2C0%2C5%2C0%29%29%2Clocate%28-1.6%2C4.75%2C3%29%2C+locate%281.4%2C4.75%2C3%29%2C+green%28line%280%2C-5%2C0%2C5%29%29%2Clocate%28-1.8%2C-3%2C4%29%2C+locate%281.6%2C-3%2C4%29%2C+locate%28.2%2C.8%2CO%29%2Ccircle%280%2C0%2C.1%29%2C%0D%0Alocate%28-3%2C0%2C5%29%2Clocate%283%2C0%2C5%29%2Clocate%28.2%2C4%2CE%29%2Clocate%28.2%2C-3%2CF%29%0D%0A%0D%0A%29

Draw in radii OA and OC, which are 5 cm each.

drawing%28200%2C200%2C-5%2C5%2C-5%2C5%2Ccircle%280%2C0%2C5%29%2Cline%28-3%2C4%2C3%2C4%29%2Cline%28-4%2C-3%2C4%2C-3%29%2C%0D%0Alocate%28-3.45%2C4.45%2CA%29%2Clocate%283.2%2C4.45%2CB%29%2C+locate%28-4.2%2C-3%2CC%29%2C+locate%284%2C-3%2CD%29%2C%0D%0Ared%28line%28-5%2C0%2C5%2C0%29%29%2Clocate%28-1.6%2C4.75%2C3%29%2C+locate%281.4%2C4.75%2C3%29%2C+green%28line%280%2C-5%2C0%2C5%29%29%2Clocate%28-1.8%2C-3%2C4%29%2C+locate%281.6%2C-3%2C4%29%2C+locate%28.2%2C.8%2CO%29%2Ccircle%280%2C0%2C.1%29%2C%0D%0Alocate%28-3%2C0%2C5%29%2Clocate%283%2C0%2C5%29%2C+blue%28line%280%2C0%2C-3%2C4%29%2Cline%280%2C0%2C-4%2C-3%29%29%2C+locate%28.2%2C4%2CE%29%2Clocate%28.2%2C-3%2CF%29%2C+locate%28-2%2C2%2C5%29%2C+locate%28-2.2%2C-.7%2C5%29%0D%0A%0D%0A%29
 
We use the Pythagorean theorem on right triangles OAE and OCF to find OE and
OF

   OA² = AE² + OE²           OC² = CF² + OF²
    5² =  3² + OE²            5² =  4² + OF²
    25 =   9 + OE²            25 =  16 + OF²
25 - 9 = OE²             25 - 16 = OF²
    16 = OE²                   9 = OF²  
     4 = OE                    3 = OF

drawing%28200%2C200%2C-5%2C5%2C-5%2C5%2Ccircle%280%2C0%2C5%29%2Cline%28-3%2C4%2C3%2C4%29%2Cline%28-4%2C-3%2C4%2C-3%29%2C%0D%0Alocate%28-3.45%2C4.45%2CA%29%2Clocate%283.2%2C4.45%2CB%29%2C+locate%28-4.2%2C-3%2CC%29%2C+locate%284%2C-3%2CD%29%2C%0D%0Ared%28line%28-5%2C0%2C5%2C0%29%29%2Clocate%28-1.6%2C4.75%2C3%29%2C+locate%281.4%2C4.75%2C3%29%2C+green%28line%280%2C-5%2C0%2C5%29%29%2Clocate%28-1.8%2C-3%2C4%29%2C+locate%281.6%2C-3%2C4%29%2C+locate%28.2%2C.8%2CO%29%2Ccircle%280%2C0%2C.1%29%2C%0D%0Alocate%28-3%2C0%2C5%29%2Clocate%283%2C0%2C5%29%2C+blue%28line%280%2C0%2C-3%2C4%29%2Cline%280%2C0%2C-4%2C-3%29%29%2C+locate%28.2%2C4%2CE%29%2Clocate%28.2%2C-3%2CF%29%2C+locate%28-2%2C2%2C5%29%2C+locate%28-2.2%2C-.7%2C5%29%2C%0D%0Alocate%28.2%2C2.5%2C4%29%2C+locate%28.2%2C-1.2%2C3%29%0D%0A%0D%0A%29

The distance between the chords = EF = OE + OF = 4 + 3 = 7cm.

Therefore it is none of the choices you gave.  The correct distance
is 7 cm.

Edwin
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