Understanding Right Triangles in Circles

The video tutorial explains the geometric properties of a circle and its diameter, focusing on a triangle where the diameter is one side. It demonstrates that such a triangle is a right triangle by using the concepts of inscribed and central angles. The tutorial also covers the properties of isosceles triangles and provides a proof that the angle opposite the diameter is a right angle.

What is the relationship between the diameter of a circle and a triangle formed with it as one side?

• The triangle is always a right triangle.

• The triangle is always scalene.

• The triangle is always equilateral.

• The triangle is always isosceles.

What is an inscribed angle in a circle?

• An angle formed by a diameter and a chord.

• An angle formed by a tangent and a chord.

• An angle formed by two chords.

• An angle formed by two radii.

How does a central angle compare to an inscribed angle subtending the same arc?

• The central angle is equal to the inscribed angle.

• The central angle is half the inscribed angle.

• The central angle is twice the inscribed angle.

• The central angle is unrelated to the inscribed angle.

In an isosceles triangle, if the top angle is 2theta, what is the expression for the base angles?

• Each base angle is theta.

• Each base angle is 90 - theta.

• Each base angle is 180 - 2theta.

• Each base angle is 2theta.

What is the sum of angles in a triangle?

• 270 degrees

• 360 degrees

• 180 degrees

• 90 degrees

What is the significance of the angle opposite the diameter in a triangle inscribed in a circle?

• It is always an acute angle.

• It is always an obtuse angle.

• It is always a right angle.

• It is always a straight angle.

What type of triangle is formed when one side is the diameter and the opposite angle is on the circumference?

• Equilateral triangle

• Isosceles triangle

• Scalene triangle

• Right triangle

What happens to the angle opposite the diameter if the vertex is moved along the circumference?

• The angle becomes acute.

• The angle remains a right angle.

• The angle becomes obtuse.

• The angle becomes a straight angle.

What is the result of the proof regarding triangles with a diameter as one side?

• The triangle is always equilateral.

• The triangle is always isosceles.

• The triangle is always a right triangle.

• The triangle is always scalene.

How can the proof be applied to different triangles with a diameter as one side?

• It only applies to scalene triangles.

• It only applies to isosceles triangles.

• It only applies to equilateral triangles.

• It applies to any triangle with a diameter as one side.