Question

В окружности с центром О АС и ВD - диаметры. Центральный угол АОD равен 74 градуса. найдите вписанный угол АСВ. Ответ дайте в градусах.

Answer 1

Проведем дополнительно BC. Следовательно углы OBC и OCB(ACB) будут равны.
Поэтому в итоге получаем: ACB=(180-74)/2=53 градуса.
п.с.: AOD=BOC как накрест лежащие если что.
п.с.2: из 180 вычитаю т.к. сумма углов в треугольнике не может превышать 180 градусов.

Answer 2

Calculating the Inscribed Angle ACB in Circle O

To find the inscribed angle ACB in circle O, given that the central angle AOD is 74 degrees, we can use the relationship between central angles and inscribed angles in a circle.

Given: - Central angle AOD = 74 degrees

Solution: 1. The measure of an inscribed angle is half the measure of its intercepted arc. 2. Therefore, the measure of the inscribed angle ACB is half the measure of the intercepted arc ADB.

Using the given information, we can calculate the measure of the inscribed angle ACB as follows:

1. Measure of the intercepted arc ADB = 2 * Central angle AOD - Measure of the intercepted arc ADB = 2 * 74 - Measure of the intercepted arc ADB = 148 degrees

2. Measure of the inscribed angle ACB = 1/2 * Measure of the intercepted arc ADB - Measure of the inscribed angle ACB = 1/2 * 148 - Measure of the inscribed angle ACB = 74 degrees

Therefore, the measure of the inscribed angle ACB in circle O is 74 degrees.