Question

A line segment drawn between points B and C on a circle forms its diameter. Point A is taken arbitrarily on the circumference of the circle, and line segments are drawn from A to B and A to C. Classify ∠BAC.(1 point)

acute angle
obtuse angle
straight angle
right angle

Answer 1

Option D

A right angle

Explanation:

in circle geometry, we have several theorems that govern angles formed by chords drawn in circles.

One of the theorems states that the angle subtended on the circumference of a circle by a chord which is drawn across the center of the circle (which is the diameter) equals 90 degrees. This means that it is a right-angle.

Analytically, we can also sketch out the problem and see that we can divide the shape formed by points BAC into an isosceles triangle. (The two radii forming the sides while the diameter forms the base). We can also run a bisector of the isosceles triangle through point A to meet the diameter. We can see that it forms two 45 by 45 degree right-angled triangles. Thus proving that angle BAC is indeed a right angle.