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A tangent PT is drawn parallel to a chord AB as shown in figure. Find the type of the triangle APB.

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Isosceles

None of the above

Equilateral

Scalene

answer is A.

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Detailed Solution

Explanation:

Given that a tangent PT is drawn parallel to a chord AB as shown in figure.

We have to find the type of the triangle APB.

The tangent-chord theorem states that the angle between a chord and a tangent through one of the endpoints of the chord is equal to the angle in the alternate segment in any circle

The required figure geometry is shown below, Question Image

From the figure $P T ‖ A B,$ so, $∠ T P A = ∠ P A B$ due to alternate angles. Therefore, $∠ T P A = ∠ A B P$ due to angles on the alternate segments.

Thus, from $∠ T P A = ∠ P A B,$ and $∠ T P A = ∠ A B P$ .

So, $∠ P A B = ∠ A B P$ .

Thus, due to sides opposite to equal angles are equal, AP = BP.

Hence, $△ A B P$ is isosceles.

Therefore, the correct option is 1.

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