The portal has been deactivated. Please contact your portal admin.

Question Video: Determining If a Circle Can Pass through Four Given Points Using the Properties of Cyclic Quadrilaterals Mathematics

Given that π‘šβˆ π΅πΆπ΄ = 61Β°, and π‘šβˆ π·π΄π΅ = 98Β°, can a circle pass through the points 𝐴, 𝐡, 𝐢, and 𝐷?

01:25

Video Transcript

Given that the measure of angle 𝐡𝐢𝐴 equals 61 degrees and the measure of angle 𝐷𝐴𝐡 equals 98 degrees, can a circle pass through the points 𝐴, 𝐡, 𝐢, and 𝐷?

Remember, if there are a pair of congruent angles subtended by the same line segment and on the same side of it, then their vertices and the segment’s endpoints lie on a circle in which that segment is a chord. Well, we have a line segment 𝐡𝐴, from which angle 𝐡𝐢𝐴 and 𝐡𝐷𝐴 are subtended. The angles lie on the same side of that line segment. So if angle 𝐡𝐢𝐴 is equal to angle 𝐡𝐷𝐴, then all four of our points must lie on the circumference of a circle. Now, we’re given that the measure of angle 𝐡𝐢𝐴 is 61 degrees and the measure of angle 𝐡𝐴𝐷 is 98.

Since triangle 𝐡𝐷𝐴 is isosceles, we can calculate the measure of angle 𝐡𝐷𝐴 by subtracting 98 from 180 and then dividing by two. And that gives us that the measure of angle 𝐡𝐷𝐴 is 41 degrees. So we see that the measure of angle 𝐡𝐢𝐴 is not equal to the measure of angle 𝐡𝐷𝐴. Since these angles are not equal, we observe that a circle cannot pass through the points, and the answer is no.

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