Question

2. Вiдрiзки АС i AB - відповідно діаметр i хорда кола iз центром 0 (мал. справа) 1) ZBAC = 26°. Знайдіть ZBOC; 2)ZBOC = 32°. Знайдіть < CAB; 3) BOA = 18°. Знайдіть COB; пж зделайтееееееееее :(​

Answer 1

Ответ:

∠ВАС - вписанный; ∠ВОС - центральный; оба эти угла опираются на дугу ВС. Вписанный угол равен половине центрального угла, опирающегося на ту же дугу, следовательно

∠ВОС = 2∠ВАС = 2*37 = 74°

Ответ: 74°

∠ВАС - вписанный; ∠ВОС - центральный; оба эти угла опираются - 1

Answer 2

Problem Statement

We have a circle with center O. Points A, B, and C are on the circumference of the circle. We are given the following information: 1. Angle ZBAC = 26°. 2. Angle ZBOC = 32°. 3. Angle BOA = 18°.

We need to find: 1. Angle ZBOC. 2. Angle CAB. 3. Angle COB.

Solution

To solve this problem, we can use the properties of angles in a circle.

1. Angle ZBOC: - Angle ZBOC is given as 32°.

2. Angle CAB: - Angle ZBAC is given as 26°. - Angle CAB is an inscribed angle that intercepts the same arc as angle ZBAC. - According to the inscribed angle theorem, the measure of an inscribed angle is half the measure of its intercepted arc. - Therefore, angle CAB = 26° / 2 = 13°.

3. Angle COB: - Angle BOA is given as 18°. - Angle COB is an inscribed angle that intercepts the same arc as angle BOA. - According to the inscribed angle theorem, the measure of an inscribed angle is half the measure of its intercepted arc. - Therefore, angle COB = 18° / 2 = 9°.

In summary, we have found the following angles: 1. Angle ZBOC = 32°. 2. Angle CAB = 13°. 3. Angle COB = 9°.

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