# Thread: If a quadrilateral is circumscribable, then the sum of the lengths of two opposite si

1. ## If a quadrilateral is circumscribable, then the sum of the lengths of two opposite si

If a quadrilateral is circumscribable, then the sum of the lengths of two opposite sides equals the sum of the lengths of the sides of the two remaining sides.

2. ## Re: If a quadrilateral is circumscribable, then the sum of the lengths of two opposit

Originally Posted by aldrincabrera
If a quadrilateral is circumscribable, then the sum of the lengths of two opposite sides equals the sum of the lengths of the sides of the two remaining sides.[/I]
Do you know the external tangent theorem: tangents from an exterior point to a circle?

3. ## Re: If a quadrilateral is circumscribable, then the sum of the lengths of two opposit

,.,.that's the thing that is making me confuse sir,.,coz i can't somehow imagine the diagram,.isn't the sum of two opposite sides longer than the sum of the other two???im confused,.,.can u help me sir??thnx

4. ## Re: If a quadrilateral is circumscribable, then the sum of the lengths of two opposit

Originally Posted by aldrincabrera
,.,.that's the thing that is making me confuse sir,.,coz i can't somehow imagine the diagram,.isn't the sum of two opposite sides longer than the sum of the other two???im confused,.,.can u help me sir??thnx
Look at the first diagram. You want to prove that $a+c=b+d.$

5. ## Re: If a quadrilateral is circumscribable, then the sum of the lengths of two opposit

,.,thnx sir,,.does this mean (always) that side a is congruent to side d??and b with c???

6. ## Re: If a quadrilateral is circumscribable, then the sum of the lengths of two opposit

Originally Posted by aldrincabrera
,.,thnx sir,,.does this mean (always) that side a is congruent to side d??and b with c???
In that diagram side a is the sum of two different line segments each tangent from external points. One those is also contained in b and the other is in d.

7. ## Re: If a quadrilateral is circumscribable, then the sum of the lengths of two opposit

,.,.thanks so much sir,.,now i have a clear perception for the proof im going to make,.,.thnx