The table below shows the amount of flour and eggs you need for making different-sized batches of cookies using the same recipe.
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Least to greatest, the triples are (2x, x²-1, x²+1). Thus the value in the first column of the table is half the value of the first of the triples. Your completed table will be
In Δ ABC, ∠A=120°, AB=AC=1
To draw a circumscribed circle Draw perpendicular bisectors of any of two sides.The point where these bisectors meet is the center of the circle.Mark the center as O.
Then join OA, OB, and OC.
Taking any one OA,OB and OC as radius draw the circumcircle.
Now, from O Draw OM⊥AB and ON⊥AC.
As chord AB and AC are equal,So OM and ON will also be equal.
The reason being that equal chords are equidistant from the center.
AM=MB=1/2 and AN=NC=1/2 [ perpendicular from the center to the chord bisects the chord.]
In Δ OMA and ΔONA
OM=ON [proved above]
OA is common.
MA=NA=1/2 [proved above]
ΔOMA≅ ONA [SSS]
∴ ∠OAN =∠OAM=60° [ CPCT]
In Δ OAN
OA=1
∴ OA=OB=OC=1, which is the radius of given Circumscribed circle.
