Question

if triangle ABC is isosceles with AB =AC prove that the tangent at A to the circumcircle of triangle ABC is a parallel to BC

Answer 1

Know the answer? Add it here!



girisai1967 Virtuoso

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

In ΔABC,
AB = AC (Given)

∴ ∠ACB = ∠ABC ...(1) (Equal sides have equal angles opposite to them)

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 BC.

I HOPE IT IS HELPFUL TO YOU

Answer 2

Step-by-step explanation:

ANSWER IN THE ATTACHMENT HOPE IT HELPED...

1. ANSWER IN THE ATTACHMENT HOPE IT HELPED...MARK ME BRAINLIEST