MATH SOLVE

2 months ago

Q:
# RQ is tangent to Circle S. Use the diagram below to find the measure of QRS. mQRS < 90 mQRS > 90 mQRS = 90 not enough information given

Accepted Solution

A:

Given that you did not include the diagram showing the circle, the tangent line and the points Q, R, and S, I am going to give you the explanation to answer the question.

1) The tangent lines to a circle form a 90° angle with the radius at the point of intersection.

2) Therefore, if the point of intersection of the tangent line and the circle is named R, and the points S and Q are one the center of the circle and the other is on the line RQ, then you know that the segment SR is a radius and the line RQ is the tangent, which means that they are perpendicular, i.e. the angle QRS is measures 90°.

In this case the answer is m angle QRS = 90°.

3) Otherwise the angle is different to 90° and you need to observe the figure to conclude whether it is greater than 90°, less than 90° or there is not enough information.

1) The tangent lines to a circle form a 90° angle with the radius at the point of intersection.

2) Therefore, if the point of intersection of the tangent line and the circle is named R, and the points S and Q are one the center of the circle and the other is on the line RQ, then you know that the segment SR is a radius and the line RQ is the tangent, which means that they are perpendicular, i.e. the angle QRS is measures 90°.

In this case the answer is m angle QRS = 90°.

3) Otherwise the angle is different to 90° and you need to observe the figure to conclude whether it is greater than 90°, less than 90° or there is not enough information.