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

• Jun 19th 2011, 07:24 PM
aldrincabrera
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.
• Jun 20th 2011, 03:18 AM
Plato
Re: If a quadrilateral is circumscribable, then the sum of the lengths of two opposit
Quote:

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?
• Jun 20th 2011, 04:11 AM
aldrincabrera
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
• Jun 20th 2011, 04:17 AM
Plato
Re: If a quadrilateral is circumscribable, then the sum of the lengths of two opposit
Quote:

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 $a+c=b+d.$
• Jun 20th 2011, 04:26 AM
aldrincabrera
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???
• Jun 20th 2011, 04:35 AM
Plato
Re: If a quadrilateral is circumscribable, then the sum of the lengths of two opposit
Quote:

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.
• Jun 20th 2011, 04:48 AM
aldrincabrera
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