Isosceles trapezoid

[westin]

Hi,

Based on the image, why when isosceles trapezoid ABCD has an incircle, then AD + BC = AB + CD (meaning the two bases added equal to the two side length)?

I could not find a properties of isosceles trapezoid that mention this relationship or it there one? Anyone that can help will be great!

Thanks.

 

[jonah2.0]

Beer induced query follows.

View attachment 34365

Hi,

Based on the image, why when isosceles trapezoid ABCD has an incircle, then AD + BC = AB + CD (meaning the two bases added equal to the two side length)?

I could not find a properties of isosceles trapezoid that mention this relationship or it there one? Anyone that can help will be great!

Thanks.

Is this problem from a textbook?
If so, what is the ISBN of your textbook?

 

[Dr.Peterson]

View attachment 34365

Hi,

Based on the image, why when isosceles trapezoid ABCD has an incircle, then AD + BC = AB + CD (meaning the two bases added equal to the two side length)?

I could not find a properties of isosceles trapezoid that mention this relationship or it there one? Anyone that can help will be great!

Thanks.

Label the four points of tangency, and use the fact that the two tangents from a given point are equal.

 

[westin]

got it. thank you