2016 · Q86
ABC is a triangle right angled at C as shown in the figure above. Which one of the following is correct?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AAQ² + AB² = BP² + PQ²
- BAQ² + PQ² = AB² + BP²
- CAQ² + BP² = AB² + PQ²
- DAQ² + AP² = BK² + KQ²
Explanation
With the right angle at C, Pythagoras gives AQ² = AC²+CQ² and BP² = BC²+CP². Also AB² = AC²+BC² and PQ² = CP²+CQ². Adding the first two and substituting the last two gives AQ²+BP² = AB²+PQ², option C.