Circles - Geometry

Card 0 of 292

Question

Calculate a point that is tangent to the circle and passes through the origin.

Answer

explain

Compare your answer with the correct one above

Question

From the following picture, determine \uptext{x}, and \uptext{y}.

Answer

Explanation

INSERT PICTURE HERE

Since this polygon is inscribed within a circle, we know a few things.

The first thing we know is that the sum of all the interior angles must equal 360^{\circ}.

The last thing we know, the most important one is all opposite angles must equal 180^{\circ}.

Now we need to set up equations to solve for \uptext{x}, and \uptext{y}.

180 = y + 117.0

180 = x + 63.0

Now let's solve for \uptext{x}, and \uptext{y}.

y = 63.0

x = 117.0

Compare your answer with the correct one above

Question

What is the measure of an inscribed angle with an arc measurement of $42 ^{\circ}$ .

Answer

The inscribed angle is simply half the arc measurement.

$\=42 \cdot \frac{1}{2} \\=21$

Compare your answer with the correct one above

Question

If the arc measure is $31 ^{\circ}$ what is the measure of the central angle?

Answer

The central angle is the same as the arc measure.

So the answer is $31 ^{\circ}$

Compare your answer with the correct one above

Question

What is the measure of an inscribed angle with an arc measurement of $54 ^{\circ}$ ?

Answer

The inscribed angle is simply half the arc measurement.

$\=54 \cdot \frac{1}{2} \\=27$

Compare your answer with the correct one above

Question

What is the measure of an inscribed angle with an arc measurement of $86 ^{\circ}$ ?

Answer

The inscribed angle is simply half the arc measurement.

$\=86 \cdot \frac{1}{2} \\=43$

Compare your answer with the correct one above

Question

Determine the area of the sector of a circle that has a central angle of degrees and a circumference of .

Refer to the following figure to help calculate the solution.

Answer

To calculate the area of the sector of the circle all that is needed is the central angle and the area of the circle. Since the central angle and circumference are given the area of the circle can be calculated.

The formulas to find the area and circumference of a circle are as follows.

$\A=\pi r^2 \C=2\pi r$

The known information is,

$\\theta =105^\circ \C=20$

Solving for the radius,

$\20=2\pi r \10=\pi r \\r=\frac{10}{\pi}$

Now the area of the whole circle is,

$\A=\pi r^2 \A=\pi \left(\frac{10}{\pi} \right )^2 \\A=\pi \times \frac{100}{\pi^2} \\A=\frac{100}{\pi}$

Now, since the question is asking for the area of the sector, a ratio will need to be constructed. Recall that a circle is composed of 360 degrees. Therefore, the following ratio can be made,

$\\frac{\theta}{360^\circ}=\frac{\text{sector area}}{\frac{100}{\pi}} \\\frac{105^\circ}{360^\circ}=\frac{\text{sector area}}{\frac{100}{\pi}} \\\frac{7}{24}=\frac{\text{sector area}}{\frac{100}{\pi}} \\\frac{7}{24}\times \frac{100}{\pi}=\text{sector area} \\\text{sector area}=9.28$

Compare your answer with the correct one above

Question

Calculate the arc length of a circle that has a central angle of degrees and a circumference of .

Refer to the following figure to help calculate the solution.

Answer

To calculate the arc length of a circle that has a central angle of degrees and a circumference of , refer to the figure and the algebraic formula for arc length.

The algebraic formula for arc length is as follows.

$s=\frac{\theta}{360^\circ}\times C$

where,

$\s=\text{Arc Length} \C=\text{Circumference} \\theta=\text{Central Angle}$

For this particular question the known information is,

$\s=\text{Arc Length} \C=16 \\theta=123^\circ$

Substitute these values into the formula and solve for the arc length.

$s=\frac{\theta}{360^\circ}\times C$

$s=\frac{123^\circ}{360^\circ}\times 16$

$s=5.4\overline{6}$

Compare your answer with the correct one above

Question

If the radius is , and the central angle is $\frac{\pi}{33}$ find the arc length.

Answer

To find the arc length, we simply multiply the radius by the central angle.

$\s = \theta r \s = 12 \cdot \frac{\pi}{33} \s = \frac{4 \pi}{11}$

Compare your answer with the correct one above

Question

Calculate the arc length of a circle that has a central angle of degrees and a circumference of .

Refer to the following figure to help calculate the solution.

Answer

To calculate the arc length of a circle that has a central angle of degrees and a circumference of , refer to the figure and the algebraic formula for arc length.

The algebraic formula for arc length is as follows.

$s=\frac{\theta}{360^\circ}\times C$

where,

$\s=\text{Arc Length} \C=\text{Circumference} \\theta=\text{Central Angle}$

For this particular question the known information is,

$\s=\text{Arc Length} \C=20 \\theta=105^\circ$

Substitute these values into the formula and solve for the arc length.

$s=\frac{\theta}{360^\circ}\times C$

$s=\frac{105^\circ}{360^\circ}\times 20$

$s=5.8\overline{3}$

Compare your answer with the correct one above

Question

If the radius is , and the central angle is $\frac{\pi}{5}$ find the arc length.

Answer

To find the arc length, we simply multiply the radius by the central angle.

$\s = \theta r \s = 13 \cdot \frac{\pi}{5} \s = \frac{13 \pi}{5}$

Compare your answer with the correct one above

Question

If the radius is , and the central angle is $\frac{\pi}{23}$ find the arc length.

Answer

To find the arc length, we simply multiply the radius by the central angle.

$\s = \theta r \s = 10 \cdot \frac{\pi}{23} \s = \frac{10 \pi}{23}$

Compare your answer with the correct one above

Question

If the radius is , and the central angle is $\frac{\pi}{23}$ find the arc length.

Answer

To find the arc length, we simply multiply the radius by the central angle.

$\s = \theta r \s = 15 \cdot \frac{\pi}{23} \s = \frac{15 \pi}{23}$

Compare your answer with the correct one above

Question

If the radius is , and the central angle is $\frac{\pi}{24}$ find the arc length.

Answer

To find the arc length, we simply multiply the radius by the central angle.

$\s = \theta r \s = 6 \cdot \frac{\pi}{24} \s = \frac{\pi}{4}$

Compare your answer with the correct one above

Question

If the radius is , and the central angle is $\frac{\pi}{31}$ find the arc length.

Answer

To find the arc length, we simply multiply the radius by the central angle.

$\s = \theta r \s = 19 \cdot \frac{\pi}{31} \s = \frac{19 \pi}{31}$

Compare your answer with the correct one above

Question

If the radius is , and the central angle is $\frac{\pi}{26}$ find the arc length.

Answer

To find the arc length, we simply multiply the radius by the central angle.

$\s = \theta r \s = 8 \cdot \frac{\pi}{26} \s = \frac{4 \pi}{13}$

Compare your answer with the correct one above

Question

If the radius is , and the central angle is $\frac{\pi}{4}$ find the arc length.

Answer

To find the arc length, we simply multiply the radius by the central angle.

$\s = \theta r \s = 19 \cdot \frac{\pi}{4} \s = \frac{19 \pi}{4}$

Compare your answer with the correct one above

Question

If the radius is , and the central angle is $\frac{\pi}{37}$ find the arc length.

Answer

To find the arc length, we simply multiply the radius by the central angle.

$\s = \theta r \s = 5 \cdot \frac{\pi}{37} \s = \frac{5 \pi}{37}$

Compare your answer with the correct one above

Question

If the radius is , and the central angle is $\frac{\pi}{24}$ find the arc length.

Answer

To find the arc length, we simply multiply the radius by the central angle.

$\s = \theta r \s = 5 \cdot \frac{\pi}{24} \s = \frac{5 \pi}{24}$

Compare your answer with the correct one above

Question

If the radius is , and the central angle is $\frac{\pi}{14}$ find the arc length.

Answer

To find the arc length, we simply multiply the radius by the central angle.

$\s = \theta r \s = 13 \cdot \frac{\pi}{14} \s = \frac{13 \pi}{14}$

Compare your answer with the correct one above

Tap the card to reveal the answer