Tangent to a Radius

Front

What is a tangent line?

Back

A tangent line is a straight line that touches a circle at exactly one point, known as the point of tangency.

Front

What is the relationship between a tangent and a radius at the point of tangency?

Back

The tangent line is perpendicular to the radius drawn to the point of tangency.

Front

If a radius measures 10 cm, what is the length of the tangent line from the endpoint of the radius to a point outside the circle?

Back

The length of the tangent line can be calculated using the Pythagorean theorem if the distance from the center to the external point is known.

Front

What is the formula to find the length of a tangent line from a point outside the circle?

Back

The length of the tangent line (t) can be found using the formula: t = √(d² - r²), where d is the distance from the external point to the center of the circle and r is the radius.

Front

What is the significance of the right angle in tangent and radius problems?

Back

The right angle indicates that the tangent line and the radius are perpendicular, which is crucial for applying the Pythagorean theorem.

Front

How do you determine if an angle is a right angle in a tangent-radius scenario?

Back

If the angle is formed between the radius and the tangent line at the point of tangency, it is a right angle.

Front

What is the length of the tangent line if the radius is 7 mm and the distance from the center to the external point is 25 mm?

Back

Using the formula: t = √(25² - 7²) = √(625 - 49) = √576 = 24 mm.

Front

What does it mean if two tangent lines are drawn from the same external point?

Back

The two tangent lines are equal in length and form two right triangles with the radius.

Front

If a tangent line is 15 cm long, what can be inferred about the distance from the external point to the center of the circle?

Back

The distance can be calculated using the formula: d = √(t² + r²), where t is the length of the tangent and r is the radius.

Front

What is the relationship between the lengths of two tangent segments drawn from the same external point?

Back

The lengths of the two tangent segments are equal.