Lesson Worksheet: Parallel Chords and Tangents in a Circle Mathematics

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In this worksheet, we will practice using the parallel chords and the parallel tangents and chords of a circle to deduce the equal measures of the arcs between them and find missing lengths or angles.

Q1:

In the given figure, the measure of , the measure of , and the measure of . What can we conclude about and ?

AThey are the same length.
BThey are parallel.
CThey are parallel and of the same length.
DThey are perpendicular.
EThey are neither parallel nor perpendicular.

Q2:

In which of these figures will be parallel to ?

Q3:

In the given figure, if the measure of arc , find the measure of arc .

Q4:

Find where is the center of the circle.

Q5:

In the following figure, a rectangle is inscribed in a circle, where the measure of . Find the measure of .

Q6:

Find the measure of the minor arc , given that the measure of the minor arc and the measure of the major arc .

Q7:

is a circle, where is a chord and is a tangent. If and the measure of , find the measure of .

Q8:

In the following figure, is a circle , and are two chords of the circle, and is a tangent to the circle at . If , the measure of , and the measure of , find the measure of .

Q9:

In the following figure, is an equilateral triangle inscribed in a circle. and are two chords of the circle, and is a tangent to the circle at . If and the measure of , find the measure of .

Find the measure of .

Q10:

In the following figure, and are two equal chords. and are two parallel chords. If the measure of , find the measure of .

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