Question Video: Finding the Measure of an Angle of Tangency given the Measure of the Inscribed Angle Subtended by the Same Arc Mathematics

Find π‘šβˆ πΆπ΄π΅.

01:12

Video Transcript

Find the measure of angle 𝐢𝐴𝐡.

First, we wanna list out the information we’re given in this diagram. We can say that line segment 𝐷𝐢 is equal to line segment 𝐴𝐢, which is equal to line segment 𝐷𝐴. Then, the line 𝐴𝐡 is tangent to the circle at point 𝐴. Using this information, we want to know the measure of angle 𝐢𝐴𝐡. From the first two given statements, there are some conclusions we can draw. First, we can say that triangle 𝐴𝐢𝐷 is equilateral. Since we know that this is an equilateral triangle, we can say that all three interior angles will measure 60 degrees. But to go any further, we need to remember the alternate segment theorem.

The alternate segment theorem tells us that the angle between a tangent and a chord is equal to the angle in the alternate segment. Our angle, angle 𝐢𝐴𝐡, is the angle between a tangent and a chord. And it will be equal to this angle in the alternate segment. And so we would say that the measure of angle 𝐢𝐴𝐡 equals 60 degrees by the alternate segment theorem.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.