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
Given : ABCD is a parallelogram and a circle is drawn through A,B and C which intersects CD produced, at E
AB=10cm BC=8cm CE=14cm
Now,
∠AED+∠ABC=1800→(1) (Sum of opposite angles of a cyclic quadrilateral is supplementary)
∠EDA+∠ADC=1800→(2) (linear pair)
∠EDA+∠ABC=1800→(3) (∵ ∠ADC=∠ABC as they are the opposite angles of a parallelogram)
From (1) & (3) we have,
∠AED=∠EDA→(4)
⇒ in ΔAED two angles are equal, hence the opposite sides corresponding to these angles must also be equal
i.e. AE=AD
and AD=BC (opposite sides of a parallelogram are equal)
∴ AE=8cm.