Question

Помогите!! Очень нужно!!! Только нужно все подробно доказывать)) В круге проведены диаметр AB и хорда CT. Докажите, что если СА = ТВ, то и СВ = ТА.

Answer 1

Можно исходить их того, что углы АСВ и АТВ -вписанные, опираются на диаметр, а значит равны 90град. Полученные прямоугольные треугольники равны по гипотенузе (АВ-диаметр) и катетам СА и ТВ (СА=ТВ по условию). Тогда равын и вторые катеты СВ=ТА 

Answer 2

I can help you with your question.

Your question is translated from Russian to English as follows:

Answer in detail. Help!! Very necessary!!! You just need to prove everything in detail)) In a circle, the diameter AB and the chord CT are drawn. Prove that if CA = TB, then CB = TA.

To prove this, we can use the following steps:

1. Draw a perpendicular bisector of CT, which will pass through the center O of the circle. 2. Since CA = TB, we have two congruent triangles OCA and OTB by SAS criterion (side-angle-side). 3. Therefore, OC = OT and angle OCA = angle OTB by CPCTC (corresponding parts of congruent triangles are congruent). 4. Since OC = OT, we have that O is the midpoint of CT. Therefore, CO = TO. 5. Since angle OCA = angle OTB, we have that angle OCB = angle OTA by subtracting angle OCT from both sides. 6. Now, we have two congruent triangles OCB and OTA by SAS criterion (side-angle-side). 7. Therefore, CB = TA by CPCTC (corresponding parts of congruent triangles are congruent). 8. Hence, we have proved that if CA = TB, then CB = TA.

I hope this helps you understand the solution. You can also check out this [website](https://online-otvet.ru/geometria/5cea758996f4e19a29fc8021) for a similar problem with a diagram. Have a nice day!