Solve this:
Q11. In the given figure, A, B, C and D, E, F are two sets of collinear points. Prove that : AD || CF.
Here is the solution of your asked query:
Q.111. Given: Two circles intersect at points B and E. A, B and C and D, E and F are collinear points.
To prove: AD CF
Proof:
Since, ABED is a cyclic quadrilateral. (points A, B, E and D lie on the circle)
So, ∠1 + ∠2 = 180° (opposite angles of a cyclic quadilateral are supplementary)
Also, ∠2 + ∠3 = 180° (linear pair)
Thus, ∠1 = ∠3 ...(i)
Now, in cyclic quadilateral BCFE,
∠3 + ∠4 = 180°
∠1 + ∠4 = 180° (using (i))
Now consider lines AD and BF and transversal AB,
Since, the sum of angles on the same side of transversal is 180°.
Hence, AD CF.
Hence proved.
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