2020 · Q87
ABC is a triangle right-angled at C. Let P be any point on AC and Q be any point on BC. Which of the following statements is/are correct?
- 1AQ² + BP² = AB² + PQ²
- 2AB = 2PQ
Select the correct answer using the code given below:
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
AQ^2+BP^2 = AC^2+CQ^2+BC^2+CP^2 = AB^2+PQ^2, so statement 1 is true; statement 2 fails for arbitrary P and Q. Statement 1 only - option (A). Statement 2 would require PQ = AB/2 for every position of P and Q, which is false (e.g. P = Q = C gives PQ = 0).