This doesn't look like a special Trapezoid!!!!

Geometry Level 3

A trapezoid A B C D ABCD has A B ∣ ∣ C D AB||CD . The lengths of segments A B AB , B C BC , C D CD and A D AD are 7 , 8 , 9 7,8,9 and 10 10 . The external bisectors of ∠ A \angle A and ∠ D \angle D meet at P P , and the external bisectors of ∠ B \angle B and ∠ C \angle C meet at Q Q . Find the length of P Q PQ .


The answer is 17.

Rayyan Shahid by Rayyan Shahid , 20, India

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2 solutions

Rayyan Shahid
Jun 25, 2015

Actually, the segment PQ is half the perimeter of trapezoid ABCD for any lengths of AB,BC,CD and AD

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Can u please tell me properties of a trapezoid if it's diagonals are at 90 degree angle... They intersect at 90.

Ayush Kumar - 3 years, 2 months ago
Aditya Kumar
Jun 24, 2015

A degenerate trapezoid. Any formal solution must include limits however to show that the points P and Q merge with the vertices and so are separated by 17.

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