ABCD is a parallelogram . The circle through A, B, and C intersects CD produced at E . If AB = 10 cm , BC = 8 cm CE = 14 cm . Find AE .
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∠AED + ∠ABC = 180 opposite angles are supplementary (1)
∠EDA + ∠ADC = 180 angles on the side of the line (2)
∠EDA + ∠ABC = 180 as ∠ADC = ∠ABC (3)
so from the equation 1 and 3
∠EDA + ∠ABC = ∠AED + ∠ABC
∠EDA = ∠AED
In ΔAED
AE = AD
so, AE = AD= BC = 8cm
as opposite sides of the parallelogram are equal
∠EDA + ∠ADC = 180 angles on the side of the line (2)
∠EDA + ∠ABC = 180 as ∠ADC = ∠ABC (3)
so from the equation 1 and 3
∠EDA + ∠ABC = ∠AED + ∠ABC
∠EDA = ∠AED
In ΔAED
AE = AD
so, AE = AD= BC = 8cm
as opposite sides of the parallelogram are equal
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