Question

What is the circumstance length? what is the length of Arc PQ? what is the length of Arc PMQ

Answer 1

In mathematics, specifically geometry, the circumference of a circle is the total distance around it and is calculated with the formula C = 2πr. The arc length of a segment of a circle can be found by using the formula (angle/360) × 2πr, with the angle being the one that subtends the arc in degrees.

Step-by-step explanation:

The question is about certain lengths associated with a circle. Firstly, the circumference length refers to the total distance around the circle. This can be calculated using the formula C = 2πr, where C is the circumference and r is the radius of the circle.

To find the length of an arc, you need to know the measure of the angle that subtends the arc (in degrees) and the radius of the circle. The formula is Arc Length = (θ/360) × 2πr, where θ is the angle in degrees. Arc PQ would refer to the length of the arc between points P and Q on the circle, which can be determined by this formula if the angle PQ is known.

Similarly, Arc PMQ refers to the length of the arc that starts at P, passes through M, and ends at Q. Again, the formula for determining arc length applies, using the angle PMQ to calculate it. It is crucial to know the measure of angle PMQ to find the precise length of Arc PMQ.

Answer 2

`\begin{gathered} \text{ Circumstance length} \\ C=2\pi r \\ C=2(3.14159)(54) \\ C=339.29172\text{ units} \\ \text{ To get the arc PQ, we have} \\ PQ=(10)/(360)(2\pi r) \\ \text{ Since we know that the circumstance is 339.29172 units} \\ \text{ we can just substitute it to }2\pi r \\ PQ=(10)/(360)(339.29172) \\ PQ=9.42477\text{ units} \\ \text{ To get arc PMQ, we have} \\ PMQ=(350)/(360)(2\pi r) \\ PMQ=(350)/(360)(339.29172)\text{ again we use the value of the circumstance earlier.} \\ PMQ=329.86695\text{ units} \end{gathered}`