Question

Отрезки AB и CD пересекаются в точке O, причём AO=DO,CO=BO. Найдите периметр треугольника AOC, если AC=4см, CD= 8см

Answer 1

СД=СО+ОД=>СО=4см, СО=ОА=4 см
Периметр=4см+4см+4см=12см

Answer 2

Solution:

Given that the segments AB and CD intersect at point O, where AO = DO and CO = BO. We are asked to find the perimeter of triangle AOC, given that AC = 4 cm and CD = 8 cm.

Steps to Solve:

1. Find the length of AD. 2. Calculate the length of BD. 3. Determine the perimeter of triangle AOC.

1. Find the length of AD: - Since AO = DO, we can conclude that triangle AOD is an isosceles triangle. - Using the property of isosceles triangles, we can find the length of AD.

The length of AD can be calculated using the property of isosceles triangles.

AD = AO + OD.

2. Calculate the length of BD: - Since CO = BO, we can conclude that triangle BOC is an isosceles triangle. - Using the property of isosceles triangles, we can find the length of BD.

The length of BD can be calculated using the property of isosceles triangles.

BD = BO + OD.

3. Determine the perimeter of triangle AOC: - Now that we have the lengths of AD and BD, we can calculate the perimeter of triangle AOC using the given length of AC.

The perimeter of triangle AOC can be calculated using the lengths of AC, AD, and CD.

Perimeter of triangle AOC = AC + AD + CD.

Calculation:

1. Find the length of AD: - AD = AO + OD - AD = AO + DO - AD = 2 * AO

2. Calculate the length of BD: - BD = BO + OD - BD = BO + DO - BD = 2 * BO

3. Determine the perimeter of triangle AOC: - Perimeter of triangle AOC = AC + AD + CD - Perimeter of triangle AOC = 4 + 2 * AO + 8

Conclusion:

The perimeter of triangle AOC, given that AC = 4 cm and CD = 8 cm, is 4 + 2 * AO + 8.