Find The Area Of My Shield

@thebigk • Oct 20, 2024

Oct 20, 2024

1.2K

Puzzle Taken From: #-Link-Snipped-#

Once upon a time, Mars, the God of war, intended to test the IQ of the goddess Minerva. So, showing his shield, he told her: "Darling, on my shield, there are 3 equal circles which represent the qualities of the warrior: strength, flexibility, and decisiveness. As you can see, one of the circles has been scratched by a sword, and the resulting score is three inches long (line AB in the illustration). Can you then tell me what is the area of my shield?".

Find the very shortest way to solve this puzzle and use only basic geometry. Trigonometry is not allowed!

area-of-shield

Discuss your answers below.

PS: I've not yet worked on this puzzle, so don't ask for clues 😛.

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Kaustubh Katdare

@thebigk • Dec 22, 2010

What? No takers? Come On People! Solve it!
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silverscorpion

@silverscorpion-iJKtdQ • Dec 22, 2010

Is the answer a number or is it an expression in R and r?
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HirenBarbhaya

@hirenbarbhaya-04r651 • Dec 22, 2010

of course.. It should be number.. as the result expected is the area... and for hint (AB line = 3) is given...
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maria flor

@maria-flor-8cAkif • Dec 23, 2010

it's really hard!!!! I've encountered such problem like that when i was 1st yr. in solid mensuration but in the problem the given is the radius of the 3 small circles...
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narayana murthy

@narayana-z4W16q • Dec 23, 2010

i think answer is R
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Kaustubh Katdare

@thebigk • Dec 23, 2010

..and the value of R is ?
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narayana murthy

@narayana-z4W16q • Dec 23, 2010

i dont know i answered as R by viewing at the diagram
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Reya

@reya-SMihdC • Dec 23, 2010

Is the answer is 186.17?
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Kaustubh Katdare

@thebigk • Dec 23, 2010

Please explain your answer.
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maria flor

@maria-flor-8cAkif • Dec 23, 2010

In finding the area of the shield A=(1/3)pi. (7+4sq.of 3)r^2 but the only problem is how to find the value of r if the only given is the chord length.

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aj_onduty

@aj-onduty-BvuwMK • Dec 23, 2010

I got the answer as 186.17 square inches. I think it is wrong as I can't explain a few things. I will post the exact answer tomorrow. Extremely sorry to say that I cannot actually work on it right now.
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maria flor

@maria-flor-8cAkif • Jan 22, 2011

I really don't know if this is correct, it is just my assumption. Since the line AB pass through the tangent of other two circle, then line AB which is 3in. is also equal to the radius of small circles. Therfore, the area of the shield would be 131.27sq.in.
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ISHAN TOPRE

@ishan-nohePN • Jan 29, 2011

The answer is 32.818inch square.
The explanation is as follows.
For smaller circle with segment AB(3 in),A total of 6 circles of same size (and all being tangents can be drawn)
so included angle between center of smaller circle(c) i.e CA and CB is 60 deg.so half the angle is 30 deg. let the mid point of AB be M. hence <MCB=<MCA=30deg.Side MA=MB=1.5inch.hence hypotenuce=r=3inch.;
and length of CM=2.598 inch.
Let the centre of bigger circle be O. hence angle between AOB=120 deg,from that length OM=.866 inch;
Now R=Radius of Bigger circle=CM+r+OM=3+2.598+.866=6.464inch;
now find the area of shield =area of Bigger circle=pi*R*R/4......(Formula of area of circle.😁😁😁
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ISHAN TOPRE

@ishan-nohePN • Jan 29, 2011

Now I deserve a chocolate from BIG_K.........
What say every one?
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maria flor

@maria-flor-8cAkif • Jan 29, 2011

The radius must be equal to 3in. Try to draw 3 equal circles with 6in. diameter. Then draw the line AB which passes through the tangent of two other circle. Try to measure from the center to the any endpoint of line AB. The line AB is equal to radius since you will form an equilateral triangle with 3in. and with an angle of 60 degree, am I right???
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ISHAN TOPRE

@ishan-nohePN • Jan 30, 2011

Hey Maria flor,You are perhaps correct..
As you are well near my answer.
Though biggie hasn't confirmed my answer yet.
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maria flor

@maria-flor-8cAkif • Jan 30, 2011

So am I correct???
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maria flor

@maria-flor-8cAkif • Jan 30, 2011

But biggie said that he doesn't know the answer. How about you try this:#-Link-Snipped-#

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maria flor

@maria-flor-8cAkif • Jun 25, 2011

Yes my answer was really correct!!!!!😁
<a href="https://www.archimedes-lab.org/monthly_puzzles_80.html" target="_blank" rel="nofollow noopener noreferrer">Previous monthly puzzles: puzzle 125</a>

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ISHAN TOPRE

@ishan-nohePN • Jun 25, 2011

So my answer correct too. 😁 exactly 131.27 as radius is correctly calculated to 6.464 inches. Congratulations maria :myparty: :myparty:
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