A geometry problem by พันดารา ธุวจิตต์

Geometry Level 3

$ABC$ is an equilateral triangle with side length of 2 cm such that three equal size circles fit in it. $O$ is the center of the circle $OD$ is perpendicular to $BC$ . What is the length of $OD$ ?

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3 solutions

พันดารา ธุวจิตต์
Mar 13, 2016

give us the more clarification . how <dop =<dcp ?

mukesh malav - 5 years, 2 months ago

Let AD ⊥ to BC then ∠ DAC = 30º ∵ OP // AC ∴ ∠DOP = ∠DAC = 30º Let CR ⊥ to AB then ∠RCB = ∠RCA = 30º ∴ ∠DCP = 30º

พันดารา ธุวจิตต์ - 5 years, 2 months ago

thanks for giving the clarification

mukesh malav - 5 years, 2 months ago

Rab Gani
Mar 19, 2019

Let the radius of the circle is r. AB = 2r + 2r√3 =2, so r=1/(1+√3). OD= r(1+√3). So OD = 1

Vedant Saini
Dec 26, 2018

NOTE: THIS IS NOT A COMPLETE SOLUTION, JUST GOING BY THE OPTIONS

$AD$ is $\sqrt{3}$ ( by applying pythagoras theorem on $\triangle ACD$ )

Thus $OD$ must be less than $\sqrt{3} \approx 1.7 \implies OD = \boxed{1}$

A geometry problem by พันดารา ธุวจิตต์

3 solutions

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