This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1910 Excerpt: ... circles, two central angles have the same ratio as the arcs intercepted by their sides. Let ABC (Fig. 155) be any central angle. By the preceding theorem it may be compared with the perigon ABA. _ ZABC arc AC.... ThenZABA = arcTMA-Why? Expressing ZABA and arc A M A by the number of units (degrees of angle and degrees ...
Read More
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1910 Excerpt: ... circles, two central angles have the same ratio as the arcs intercepted by their sides. Let ABC (Fig. 155) be any central angle. By the preceding theorem it may be compared with the perigon ABA. _ ZABC arc AC.... ThenZABA = arcTMA-Why? Expressing ZABA and arc A M A by the number of units (degrees of angle and degrees of arc) they contain, respectively, we have ZABCarc AC 360 360 Multiplying through by 360, ZABC = arc AC, in the sense that the number of angle degrees in Z A B C is the same as the number of arc degrees in the arc A C. As A B C is any central angle, the number of degrees in any central angle is the same as the number of degrees in the arc intercepted by its sides. This is more technically stated thus: Proposition II 159. Theorem: A central angle is measured by the arc intercepted by its sides. Exercises 160. Solve the following exercises: 1. By Proposition II, using rule and compasses only, divide a circle (a) into 4 equal arcs; (b) into 2 equal arcs. 2. Divide a circle into three arcs in the ratio of i: 2: 3. 3. Find an arc of 450; 750; 1050; 1650; 150. 4. If a circle is divided into 4 arcs in the ratio of 1: 4: 6: 7 what is the number of degrees in each arc? 5. The area of a circle is 616 sq. in. How many degrees are there in an angle at the center that intercepts an arc 11 in. long? Assume area of circle = TR2 and circumference = 2tr. Use r=fy. 6. In Fig. 156, A B is a diameter. The number of degrees in angle A O C and B O C are represented by x2]4X and 32 +12x. Find the values of x and the number of degrees in arcs A C and B C. A B Fig. 156 Fig. 157 7. In Fig. 157, ZABC is a right angle. ZABD = 2X2--3, and ZD B C = io2-i5. Find the values of x and the number of degrees in arcs A D and D C. Inscribed Angles 161. Let us next consider what r...
Read Less
