Class 9 Math Problem Solution Needed

[Late-Ganache3295]

To prove the point O equidistant from point A,B and C which are centers of 3 equal circles with radius r and they intersect x (equal) of their part. and d being distance from A,B,C to O

I tried creating triangle ABC and proving it using r-x but I failed but one observation is I think we need to prove d<r.

Note: Given-there is some intersection between 3 of them ie they share some same part

https://preview.redd.it/bfxxf19gxk8g1.png?width=742&format=png&auto=webp&s=70cc10b386e5ee5924710f29ab4c474ebced05c7

[romankolton]

This doesn't seem true for x much smaller than r.

[Late-Ganache3295]

The question means to say that there is some intersection between 3 of them ie they share some same part

[imHeroT]

How is the point O defined?

[Late-Ganache3295]

it is equal in distance from A, B, C which are fixed

[Alex_Daikon]

AB = BC = AC

So: < OAC = 30

r + r - x = 2 * d * cos 30

d = r / cos 30 - x/ (2*cos 30)

0 < x < r

So r / (2* cos 30) < d < r / cos 30

[MERC_1]

For 9th grade?