# Find The Area Of My Shield

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

## Replies

• Kaustubh Katdare
What? No takers? Come On People! Solve it!
• silverscorpion
Is the answer a number or is it an expression in R and r?
• HirenBarbhaya
of course.. It should be number.. as the result expected is the area... and for hint (AB line = 3) is given...
• maria flor
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...
• narayana murthy
• Kaustubh Katdare
..and the value of R is ?
• narayana murthy
i dont know i answered as R by viewing at the diagram
• Reya
• Kaustubh Katdare
• maria flor
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
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.
• maria flor
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.
• ISHAN TOPRE
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 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 find the area of shield =area of Bigger circle=pi*R*R/4......(Formula of area of circle.😁😁😁
• ISHAN TOPRE
Now I deserve a chocolate from BIG_K.........
What say every one?
• maria flor
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???
• ISHAN TOPRE
Hey Maria flor,You are perhaps correct..
As you are well near my answer.
Though biggie hasn't confirmed my answer yet.
• maria flor
So am I correct???
• maria flor
• maria flor
Yes my answer was really correct!!!!!😁
Previous monthly puzzles: puzzle 125
• ISHAN TOPRE
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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