Question

"в треугольнике ABC CH -высота , AD -биссектриса , O-точка пересечения прямых CH и AD ,угол BAD= 26 найдите угол AOC"

Answer 1

Если CH -высота, то ΔАОH-прямоугольный, ⇒ угол АОН=90-26=64
углы АОН и АОС -смежные⇒ угол АОН +угол АОС=180°
угол АОС=180-угол АОН=180-64=116
отв:116

Answer 2

Given Information:

In triangle ABC, CH is the height, AD is the bisector, and O is the point of intersection of the lines CH and AD. The angle BAD is 26 degrees. We need to find the angle AOC.

Solution:

To find the angle AOC, we can use the fact that the sum of the angles in a triangle is 180 degrees. We can start by finding the angles in triangle ABC.

Let's denote the angle BAC as angle A, angle ABC as angle B, and angle BCA as angle C.

Since CH is the height, it is perpendicular to the base AB. Therefore, angle ACH is a right angle, which means angle BAC is also a right angle.

We are given that angle BAD is 26 degrees. Since AD is the bisector, angle BAD is equal to angle CAD. Therefore, angle CAD is also 26 degrees.

Using the fact that the sum of the angles in a triangle is 180 degrees, we can write the following equation:

angle A + angle B + angle C = 180 degrees

Since angle BAC is a right angle, it is equal to 90 degrees. Therefore, we can rewrite the equation as:

90 degrees + angle B + angle C = 180 degrees

Simplifying the equation, we get:

angle B + angle C = 90 degrees

Now, let's consider triangle AOC. We need to find the angle AOC.

Since angle BAC is a right angle, angle BOC is also a right angle. Therefore, angle BOC is equal to 90 degrees.

Using the fact that the sum of the angles in a triangle is 180 degrees, we can write the following equation for triangle AOC:

angle AOC + angle OAC + angle OCA = 180 degrees

Since angle OAC is equal to angle CAD (26 degrees) and angle OCA is equal to angle BAC (90 degrees), we can rewrite the equation as:

angle AOC + 26 degrees + 90 degrees = 180 degrees

Simplifying the equation, we get:

angle AOC = 180 degrees - 26 degrees - 90 degrees

angle AOC = 64 degrees

Therefore, the angle AOC is 64 degrees.

Answer: The angle AOC is 64 degrees.