Geometriia Kniga Ershovoi Str 167 Variant A2 8 Klass Guide

According to the theorem on inscribed angles, an inscribed angle is equal to half of the central angle that subtends the same arc.

∠ABC=12⋅∠AOCangle cap A cap B cap C equals one-half center dot angle cap A cap O cap C

Substitute the given value of the central angle: geometriia kniga ershovoi str 167 variant a2 8 klass

For , the specific problem (usually task #2 or #3 in this section) involves calculating angles related to a circle or inscribed polygons. Problem Statement (Typical for Variant A2, Page 167) Task: Points lie on a circle with center . The central angle ∠AOCangle cap A cap O cap C 140∘140 raised to the composed with power . Find the inscribed angle ∠ABCangle cap A cap B cap C lies on the major arc ACcap A cap C Solution Steps

∠ABC=12⋅140∘=70∘angle cap A cap B cap C equals one-half center dot 140 raised to the composed with power equals 70 raised to the composed with power Since point According to the theorem on inscribed angles, an

The following graph illustrates the relationship between the central angle ( ∠AOCangle cap A cap O cap C ) and the inscribed angle ( ∠ABCangle cap A cap B cap C ) subtending the same arc. Final Answer ✅ The inscribed angle ∠ABCangle cap A cap B cap C 70∘70 raised to the composed with power АЛГЕБРА ГЕОМЕТРИЯ

is on the major arc, the inscribed angle subtends the minor arc ACcap A cap C . The calculation above is correct for this configuration. Educational Visualization The central angle ∠AOCangle cap A cap O

Based on the popular textbook by A.P. Ershova and V.V. Goloborodko, page 167 typically contains problems from Self-study Work S-13 (or the end of S-12), which focuses on the properties of Central and Inscribed Angles in a circle.