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  • In fig.7 two equal circles , with center O and O' , touch each other at X. OO' produce meets the circle with center O' at A . AC is tangent  to the circle with center O , at the point C. O'D is perpendicular to AC. Find the va

In fig.7 two equal circles , with center O and O' , touch each other at X. OO' produce meets the circle with center O' at A . AC is tangent  to the circle with center O , at the point C. O'D is perpendicular to AC. Find the value of \frac{DO'}{CO}

 

 

 

 
 
 
 
 

Answers (1)

Given = radius of both circles are equal 

radius = r 

O'D \perp AC \\\\ \angle O'DA = 90 \degree \\\\ to\: \: find \: \: DO'/CO= ?

Also as AC is tangent to circle with center O 

then AC \perp OC 

\angle OCA = 90 \degree

Now in \Delta AO'D and \Delta AOC

\angle O'DA = \angle OCA = 90 \degree \\\\ \angle A = \angle A

By AA similarity , 

\Delta A O'D \sim \Delta AOC\\\\ \frac{DO'}{CO}= \frac{AO'}{AO}\\\\ Now \: \: AO = r+r+r = 3r \\\\ \frac{DO'}{CO}= \frac{AO'}{AO}=\frac{1}{3}

Posted by

Ravindra Pindel

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