Exploring Circle Theorems

Equal chords are equidistant from the center.

True or False

Equal Chords are equidistant from any point on the circle.

False True

True / False

Mark/ Write the statement which is not True

Longest Chord in a quadrant always subtend an angle of 90[math]^\circ[/math] at the center Diameter is the longest chord Larger of the chords is farther from the center Equal Chords are equidistant from the center

Extended Response

Prove that Equal chords subtend equal angles at the center of the circle. Click a picture of your hand written proof and paste (jpg/pdf) on the worksheet on MS Teams Assignment Link /Page!

Perpendicular from the center of the circle bisects the chord. Explore the applet by dragging the points.

True or False

Only chords pertaining to Minor Arcs are bisected by the perpendicular from the center of the circle.

True False

Choose the correct Option

If a line drawn from the center of the circle meets the midpoint of the chord. then

Line makes an angle of 90[math]^\circ[/math] with the chord Line is the shortest distance to the chord Line is perpendicular to the chord All of the above

Angles in the same segment are equal in magnitude

MCQ

Which of the following are true about a circle?

Angle on a major arc is acute None of the above Angle on a minor arc is obtuse Angle in a semi circle is always 180[math]^\circ[/math]

Choose the correct option

Angle subtended by a chord in a semi circle is 90[math]^\circ[/math]

Never True Always True Only when chord is perpendicular to the line from the center of the circle Only when chord is the diameter

Write down the detailed proof for the subject theorem- Angles in the same segment are equal in measurement. (Paste (jpg/pdf) your response on the One Note link/page

Equal Chords subtend equal angles at the center

Choose the statements that are correct

If two arcs of a circle are equal then:

Arcs are congruent their corresponding chords are equal Subtend equal angles at the center None of above

Exploring Circle Theorems

Equal chords are equidistant from the center.

True or False

True / False

Extended Response

Perpendicular from the center of the circle bisects the chord. Explore the applet by dragging the points.

True or False

Choose the correct Option

Angles in the same segment are equal in magnitude

MCQ

Choose the correct option

Write down the detailed proof for the subject theorem- Angles in the same segment are equal in measurement. (Paste (jpg/pdf) your response on the One Note link/page

Equal Chords subtend equal angles at the center

Choose the statements that are correct

Angle subtended by the chord at the center is double the angle subtended at the circle.

Reflection

Information: Exploring Circle Theorems