Question

plsss answer fast..plsss

Answer 1

in this figure I will the theorem:the angle between the chord and the tangent is equal to the angle in the alternate segment of the chord.so ang.bap is equal to ang BCA
and ang.cat is equal to ABC
therefore ang bap is equal to ang cat
and ang BCA is equal to ang bap or cat
thus a pair of alternate angles
and hence parrellel.

Answer 2

Heya!!
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PAT 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, PAT is the tangent and AB is the chord.

∴ ∠PAB = ∠ACB ...(2)

From (1) and (2), we have

∠ABC = ∠PAB

∴ PT || 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.


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# hope this helps you!