A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc.

Sure, here are the steps to find the angle subtended by the chord at a point on the major arc:

1. Draw a circle and mark the center as O. Draw a radius of the circle and mark the end point on the circle as A.

2. Draw a chord of the circle that is equal in length to the radius. Mark the end points of the chord as B and C.

3. Draw the radii OB and OC. Now, you have an isosceles triangle OBC because OB = OC (both are radii of the circle) and BC = OA (given that the chord is equal to the radius).

4. In an isosceles triangle, the base angles are equal. Therefore, ∠BOC = ∠BCO.

5. The sum of the angles in a triangle is 180 degrees. Therefore, ∠BOC + ∠BCO + ∠B = 180 degrees.

6. Substituting ∠BCO for ∠BOC gives 2∠BOC + ∠B = 180 degrees.

7. The angle subtended by the chord at the center of the circle is 2 times the angle subtended by the chord at any point on the alternate arc. Therefore, ∠B = 2∠BAO.

8. Substituting 2∠BAO for ∠B in the equation from step 6 gives 2∠BOC + 2∠BAO = 180 degrees.

9. Simplifying gives ∠BOC + ∠BAO = 90 degrees.

10. Therefore, the angle subtended by the chord at a point on the major arc is 90 degrees.