Question

трикутник АВС вписаний у коло центр якого лежить на відрізку АВ . знайдіть міри кутів С і В якщо кут А=52°​

Answer 1

Кут А = 90 градусів (AB - радіус) кут С = 180-90-52=36 градусів

Answer 2

Ответ:

С = 180-52-90 =36 градусі

Answer 3

Triangle ABC Inscribed in a Circle

To find the measures of angles C and B in triangle ABC, we need to consider the properties of a triangle inscribed in a circle.

In a triangle inscribed in a circle, the measure of an angle formed by a chord is half the measure of the intercepted arc. This property is known as the Inscribed Angle Theorem.

Given that angle A is 52°, we can use the Inscribed Angle Theorem to find the measures of angles C and B.

Solution:

1. Let's assume that the center of the circle is O, and the point where the circle intersects segment AB is D.

2. Since angle A is 52°, the intercepted arc AD is also 52°.

3. According to the Inscribed Angle Theorem, angle C is half the measure of the intercepted arc AD. Therefore, angle C is 26°.

4. Similarly, angle B is half the measure of the intercepted arc BD. Since the intercepted arc BD is the complement of arc AD, its measure is 180° - 52° = 128°. Therefore, angle B is half of 128°, which is 64°.

Therefore, the measures of angles C and B in triangle ABC are 26° and 64°, respectively.

Please let me know if you have any further questions!