Here are the answers to the questions provided:
Question 1: A circle has a center point C. Points D, E, F, and G lie on the circumference of the circle.
If CH = 42 m and CF = 58 m, then what is the length of FG?
Answer: 16 m
Question 2: A circle has center point O. O connects to a point on the circumference labeled B. B connects to a point outside the circle labeled A.
If BO = 45 in. and BA = 108 in., then what is the length of AO to the nearest whole inch?
Answer: 98 in
Question 3: A circle has a center point marked as G. Points H, I, J, and K lie on the circumference of the circle.
If arc KJ = 13x - 10 and arc JI = 7x - 10, then find the m∠KIJ.
Assuming that m∠KIJ = (arc KJ + arc JI)/2, we find:
Answer: 80°
Question 4: Triangle XYZ is inscribed inside a circle with diameter XZ and the inscribed angle at Y. The angle measure at X is 59°.
Using what you know about inscribed angles, find the arc measure of XY.
The arc measure of XY will be double the angle at Y.
Answer: 118°
Question 5: Quadrilateral ABCD is drawn within a circle such that all vertices touch the edge of the circle.
The m∠B is 93°, the measure of arc BC is 58°, and the measure of arc CD is 106°. Find the measure of ∠A.
Using opposite angles in a cyclic quadrilateral: ∠A + ∠C + 93° + (1/2)(106°) = 180°
Answer: 106°
Question 6: Same conditions as Question 5. Find the measure of ∠C.
Using opposite angles in cyclic quadrilateral: ∠A + ∠C + 93° + (1/2)(58°) = 180°
Answer: 98°
Question 7: Same conditions as Question 5. Find the measure of ∠D.
Using angles in a cyclic quadrilateral: ∠D + 93° + (1/2)(106°) + (1/2)(58°) = 180°
Answer: 87°
Question 8: Jamila wants to know the length of the circular path with a walkway across it being 12 miles.
The diameter is 12 miles, therefore the circumference is C = πd.
Answer: 37.7 mi (which rounds up to 3.1 mi for the closest tenth of a mile)
Question 9: If the area of a circle is 586 m², then what is the length of the diameter to the nearest meter?
A = πr² → 586 = πr² → r² = 586/π → r = √(586/π) → d = 2r.
Answer: 27 m
Question 10: If a circle has a central angle of 125° and a radius of 27 millimeters, how long is the arc formed by that angle?
Arc Length Formula: L = (θ/360°) * 2πr.
Answer: 75π/4 mm
Question 11: What is the area of the sector of a circle with a central angle of 216° and a radius of 7 inches?
Area of a Sector Formula: A = (θ/360°) * πr².
Answer: 26.4 inches
Question 12: A cookie cake has a diameter of 18 in. If part of the cookie cake is eaten, the missing section forms an angle of 270°.
Area of Circle: A = πr²; Area eaten = (270/360) * Area of Cake.
Answer: 127.2 in²
These answers sum up various properties of circles, angles, and sectors based on the inputs provided for each question.
1 answer