Geometry of Circles - Review Set 21

What is the value of x if 56 + x = 142?

Using Pythagoras' theorem, what is the radius OB if BM = 5 cm and OB = OA = x?

How do you express the relationship between obtuse BOD and angle BAD?

What value do you get for angle AOC if AOC + 250° = 360°?

In triangle AOC, if the angles are x, x, and 70°, what is the value of x?

Given the equation 4x + 36 = 180, what is the value of x?

If y - 22 + y + 34 + y = 180, what is the value of y?

What is the approximate diameter FD of the circle if sin 56° = 5.5 / FD?

What is the value of angle BOC when BAC is 36°?

If angles ABC, ABO, and AOB form a triangle and ABC is a right angle, what is the value of angle AOB if angle ABC is 90°?

Given that ACD and ABD are angles on the same arc, what is their common value?

In triangle ABC, if the two angles are expressed as x and x + 14, what is the value of x?

What is the relationship between angle ABC and angle AOC given that AOC measures 120°?

If angles CAB and CBA are both 38°, what is the value of x in triangle AABC?

In triangle ABC, if angles ACB and ABC satisfy the equation α + β = 90°, what does this imply about triangle ABC?

What relationship can be established between angles AOB and ACB through the circle?

Review Set 21 - Geometry of Circles

Angle at the Centre: The angle at the centre of a circle is twice the angle at the circumference subtended by the same arc.
Isosceles Triangles: In a circle, if two radii are equal, the triangle formed by connecting the centre and the endpoints of the radii is isosceles. Base angles of an isosceles triangle are equal.
Angles in a Triangle: The sum of the angles in any triangle is 180 degrees.
Angles in a Semi-Circle: An angle in a semi-circle is a right angle (90 degrees).
Tangent and Chord: The angle between a tangent and a chord drawn from the point of tangency is equal to the angle subtended by the chord in the alternate segment.
Tangents from an External Point: Tangents drawn from an external point to a circle are equal in length.
Midpoint of a Chord: The perpendicular bisector of a chord passes through the centre of the circle.

Practice Test 21B

Angles on Same Arc: Angles subtended by the same arc at the circumference are equal
Exterior Angle of a Triangle: The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Pythagorean Theorem: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. a² + b² = c².
Radii: Radii of a circle are all equal in length.

This quiz covers essential concepts of circle geometry, including angles at the center, isosceles triangles formed by radii, and properties of tangents and chords. Test your understanding of how angles relate in a circle and the significance of tangent lines. Perfect for reinforcing knowledge in geometry!