Please solve question no.36.

Dear Student

Let DAE be tangent at A to the circumcircle of ΔABC.

In ΔABC,

AB = AC     (Given)

∴ ∠ACB = ∠ABC   ...(1)        (Angle opposite to equal sides are equal)

We know that, If a line touches a circle and from the point of contact, a chord is drawn, then the angles between the tangent and the chord are respectively equal to the angles in the corresponding alternative segment.

Now, DAE is the tangent and AB is the chord.

∴ ∠DAB = ∠ACB    ...(2)

From (1) and (2), we have

∠ABC = ∠DAB

∴ DE || BC     (If a transversal intersects two lines in such a way that a pair of alternate interior angles are equal, then the two lines are parallel)

Thus, the tangent at A to the circumcircle of  ΔABC is parallel to BC.


Regards