Mathematics

Mathematics

Problem

A brooch is a decorative piece often worn on clothing like jackets, blouses or dresses to add elegance. Made from precious metals and decorated with gemstones, brooches come in many shapes and designs. ![A grid of 20 colorful, circular brooch designs, illustrating various shapes and patterns.](https://storage.googleapis.com/diraq-contents/homework-question-parsing/marker/20260107T161002Z/49a4004a2f594251b7d59422af8e65f4/56a7fc5964ed9463fa47ca8a60568dec_img.jpg) One such brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in the figure. ![Diagram of a circular brooch divided into 10 equal sectors by 5 diameters. Points A, B, and C are marked on the circumference.](https://storage.googleapis.com/diraq-contents/homework-question-parsing/marker/20260107T161002Z/d6e4ffd38c304b29b4c76161348ed3d8/d4c143a69ccd7e28fe8d01dbc9dfbcfa_img.jpg) Based on the above given information, answer the following questions : a. Find the central angle of each sector. b. Find the length of the arc ACB. c. (a) Find the area of each sector of the brooch. d. OR (b) Find the total length of the silver wire used.

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