Question

Write True or False:

The tangent to the circumcircle of an isosceles $△ABC$ at A, in which $AB=AC$, is parallel to BC.

• A. True
• B. False
• C. Ambiguous
• D. Data insufficient

Answer 1

The correct option is A True

Given-

PQ is a tangent to a circle at a point A when the circle is a circumcircle of the isosceles $\Delta ABC$.

$AB=AC.$

To find out -

The statement, $PQ\parallel BC$, is true or not.

Justification-

In $\Delta ABC$ we have,

$AB=AC.$

$\therefore \angle ABC=\angle ACB$ ...(base angles of an isosceles triangle) ........(i)

Again, PQ is the tangent to the circle at A & AB is a chord drawn from A.

And AB subtends \angle ACB to the corresponding alternate segment of the circle.

$\therefore \angle PAB=$ corresponding alt. segment $\angle ACB$ ......(ii)

So, from (i) & (ii),

$\angle PAB=\angle ABC.$

But they are alternate angles $⟹PQ\parallel BC$

$\therefore$ The statement, $PQ\parallel BC$, is true.