Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Geometry explanation help.?
I have to explain why this is correct, but I don't know how to explain it. Help please. I have to explain why this sentence is true: A chord-tangent angle is half of the arc, it spans. I will include a picture if it will help. A is twice the size of B.
1 Answer
- 7 years agoFavorite Answer
This is so easy, you may kick yourself when you see the answer.
The triangle inside the circle (composed of the two radii and the chord) must have internal angles that sum to 180°
One of the three is ∠A
The triangle is isosceles (two sides equal to circle radius), so the other two internal angles (48.1° in this case) must be equal to each other.
Let both of these angles be ∠φ
So we have ∠A+∠φ+∠φ= ∠A+2∠φ= 180°
But at the tangent to the circumference, we also have ∠B+∠φ= 90°
From which ∠φ= 90°-∠B.
Replace for ∠φ in the sum for the triangle, with the following steps we then get:
∠A+2(90°-∠B)= 180°
∠A+180°-2∠B= 180°
∠A-2∠B= 0
∠A=2∠B, or ½∠A=∠B
Job done.