solve this

Geometry Level 2

LET ABCD BE A UNIT SQUARE. DRAW A QUADRANT OF A CIRCLE WITH A AS CENTRE AND B,D AS END POINTS OF THE ARC. SIMILARLY,DRAW A QUADRANT OF A CIRCLE WITH B AS THE CENTRE AND A,C AS END POINTS OF THE ARC .INSCRIBE A CIRCLE WITH RADIUS r TOUCHING THE ARCS AC AND BD BOTH EXTERNALLY AND ALSO TOUCHING THE SIDE CD . FIND THE RADIUS OF THE CIRCLE WITH RADIUS r r=?


The answer is 0.0625.

Abhishek Sahoo by ABHISHEK Sahoo , 20, India

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1 solution

Pranjal Jain
Jan 19, 2015

Let bottom right corner be O and centre of smaller circle be O', foot of perpendicular from O' on AB be P.

  • OO' = 1 + r =1+r
  • OP = 1 2 =\dfrac{1}{2}
  • O'P = 1 − r =1-r

Apply Pythagoras theorem in △ \triangle OO'P,

( 1 + r ) 2 = ( 1 − r ) 2 + ( 1 2 ) 2 (1+r)^2=(1-r)^2+(\frac{1}{2})^2 Solving, we get r = 1 16 r=\dfrac{1}{16}

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@ABHISHEK Please refrain from using capital letters. They are used as in "shouting" on internet and seems disrespectful.

Pranjal Jain - 6 years, 4 months ago

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am guilty for this sorry

ABHISHEK Sahoo - 6 years, 4 months ago

5^4×10^-4 is the radius of the small circle.

Akshat Sharda - 6 years ago

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