What is the relationship between the angles formed by two tangents drawn from a

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Question: What is the relationship between the angles formed by two tangents drawn from a point outside a circle?

Options:

Correct Answer: They are equal

Solution:

The angles formed by two tangents drawn from a point outside a circle to the points of tangency are equal.

What is the relationship between the angles formed by two tangents drawn from a point outside a circle?

What is the relationship between the angles formed by two tangents drawn from a point outside a circle?

Step 1: Understand what a tangent is. A tangent is a line that touches a circle at exactly one point.
Step 2: Identify the point outside the circle from which the tangents are drawn. Let's call this point P.
Step 3: Draw two tangents from point P to the circle. Let's call the points where the tangents touch the circle A and B.
Step 4: Notice that the two tangents PA and PB are equal in length. This is a property of tangents from a common external point.
Step 5: Look at the angles formed at point P. These angles are ∠APB (the angle between the two tangents).
Step 6: Understand that the angles formed at points A and B (the points of tangency) with the radius of the circle are right angles (90 degrees).
Step 7: Use the property of isosceles triangles. Since PA = PB, the angles ∠PAB and ∠PBA are equal.
Step 8: Conclude that the angle ∠APB is equal to the sum of the angles ∠PAB and ∠PBA, which means the angles formed by the two tangents are equal.

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