Circle Arcs and Sectors
Circle arcs and sectors play a fundamental role in geometry, offering insights into the properties and measurements of circular shapes. An arc is a curved portion of a circle, defined by two endpoints on the circle's circumference. Sectors, on the other hand, are portions enclosed by two radii and the corresponding arc, resembling a slice of the circular whole. Understanding the relationships between angles, arc lengths, and sector areas in circles is crucial for various mathematical applications, ranging from geometry problems to real-world scenarios involving circular objects and spaces.
Questions
- A circle has a chord that goes from #pi/4 # to #pi/2 # radians on the circle. If the area of the circle is #48 pi #, what is the length of the chord?
- A circle has a chord that goes from #( 3 pi)/8 # to #(5 pi) / 3 # radians on the circle. If the area of the circle is #36 pi #, what is the length of the chord?
- A circle's center is at #(2 ,4 )# and it passes through #(7 ,6 )#. What is the length of an arc covering #(15pi ) /8 # radians on the circle?
- A circle's center is at #(2 ,6 )# and it passes through #(3 ,1 )#. What is the length of an arc covering #(2pi ) /3 # radians on the circle?
- A circle has a chord that goes from #( pi)/6 # to #(11 pi) / 8 # radians on the circle. If the area of the circle is #64 pi #, what is the length of the chord?
- In the figure, M is a center of the circle, F is the intersection of the lines AC and BD, and E is the intersection of the lines CM and BD. The line CM is perpendicular to the line BD. If the measure of angle MBE is #32^o#, the measure of angle CFD is . ?
- Points #(8 ,5 )# and #(3 ,4 )# are #( pi)/3 # radians apart on a circle. What is the shortest arc length between the points?
- A circle has a chord that goes from #( 3 pi)/8 # to #(4 pi) / 3 # radians on the circle. If the area of the circle is #48 pi #, what is the length of the chord?
- The circumference of a circle is #88pi# #cm#. What is the radius, and the length of an arc that is 40°?
- Points #(2 ,6 )# and #(5 ,9 )# are #(3 pi)/4 # radians apart on a circle. What is the shortest arc length between the points?
- A circle has a center at #(7 ,6 )# and passes through #(2 ,1 )#. What is the length of an arc covering #pi/12# radians on the circle?
- A circle has a chord that goes from #( pi)/3 # to #(7 pi) / 8 # radians on the circle. If the area of the circle is #16 pi #, what is the length of the chord?
- A circle has a chord that goes from #( pi)/2 # to #(15 pi) / 8 # radians on the circle. If the area of the circle is #48 pi #, what is the length of the chord?
- Points #(2 ,9 )# and #(1 ,5 )# are #(3 pi)/4 # radians apart on a circle. What is the shortest arc length between the points?
- A circle has a chord that goes from #pi/3 # to #(3 pi) / 8 # radians on the circle. If the area of the circle is #81 pi #, what is the length of the chord?
- A circle has a chord that goes from #( 4 pi)/3 # to #(17 pi) / 12 # radians on the circle. If the area of the circle is #27 pi #, what is the length of the chord?
- A circle has a chord that goes from #( 2 pi)/3 # to #(17 pi) / 12 # radians on the circle. If the area of the circle is #9 pi #, what is the length of the chord?
- A circle has a chord that goes from #( pi)/3 # to #(2 pi) / 3 # radians on the circle. If the area of the circle is #16 pi #, what is the length of the chord?
- Points #(6 ,2 )# and #(1 ,5 )# are #(2 pi)/3 # radians apart on a circle. What is the shortest arc length between the points?
- A circle's center is at #(7 ,2 )# and it passes through #(5 ,6 )#. What is the length of an arc covering #(7pi ) /4 # radians on the circle?