Question

ABCD is a parallelogram the circle through A,B,C intersect CD produced at E.if AB= 10,BC =8 cm ,CE=14 cm and find AE .

Answer 1

Answer: 8 cm

Step-by-step explanation: pls look the diagram attached for clear idea.

Now in quad. EABC,

∠AED + ∠ABC = 180°(Opposite angles of a cyclic quad.).......(1)

Also, ∠EDA + ∠ADC = 180°(Linear pair).........(2)

But we know ∠ABC = ∠ADC ( Opp. angles of a parallelogram)........(3)

From (1), (2) and (3)

∠AED = ∠ADE

So, AE = AD (Sides opp. to equal angles are equal)......(4)

But we know AD = BC (Opposite sides of a parallelogram).........(5)

From (4) and (5),

AE = BC

Since BC is given as 8 cm,

Therefore AE = 8cm.

Pls mark brainliest if you like.

Answer 2

Answer:

Step-by-step explanation:

∠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