Question

Между сторонами угла DOA проведено лучи ОС и ОВ так, что угол СОD: угол АОВ= 3:4, а угол ВОС=1/3*СОD. Докажите, что ОВ или ОС биссектрисы угла АОD.

Answer 1

Пошаговое объяснение:

1)10^:5=5×10=50^55=(5×10)+(10^:5)×50^50=16946826

Answer 2

Given Information:

We are given that there is an angle DOA, and rays OS and OV are drawn such that the angle COD is in a ratio of 3:4 with the angle AOV, and the angle VOS is equal to 1/3 times the angle COD.

To Prove:

We need to prove that either OV or OS is the bisector of angle AOD.

Proof:

Let's assume that OV is the bisector of angle AOD.

According to the angle bisector theorem, the ratio of the lengths of the segments formed by the angle bisector is equal to the ratio of the lengths of the opposite sides of the angle. In this case, we have:

AO/OB = AD/DB (1)

Now, let's consider the given ratios:

COD:AOV = 3:4 (2)

VOS = 1/3 * COD (3)

From equation (2), we can express AOV in terms of COD:

AOV = (4/3) * COD (4)

Substituting equation (4) into equation (1), we have:

AO/(OB) = AD/DB = (4/3) * COD / (COD - (4/3) * COD)

Simplifying the equation, we get:

AO/(OB) = AD/DB = 4/3

This implies that the ratio of the lengths of AO and OB is equal to the ratio of the lengths of AD and DB. Therefore, OV is the bisector of angle AOD.

Hence, we have proved that OV is the bisector of angle AOD.

Note: The same proof can be applied to show that OS is also the bisector of angle AOD.