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?<br>1. AQ^{2}+BP^{2}=AB^{2}+PQ^{2}<br>2. AB=2PQ<br>Select the correct answer using the code given below:
- A. 1 only ✓
- B. 2 only
- C. Both 1 and 2
- D. Neither 1 nor 2
Correct Answer: A. 1 only
Explanation
Applying Pythagoras in \Delta ACQ, AQ^2 = AC^2 + CQ^2. In \Delta PCB, BP^2 = PC^2 + BC^2. Adding these gives AQ^2 + BP^2 = (AC^2 + BC^2) + (CQ^2 + PC^2). This simplifies perfectly to AB^2 + PQ^2. Stmt 2 is generally false for arbitrary points P and Q.
Related questions on Geometry
- In a triangle ABC, \angle A = 30^\circ, AB = 7 cm and AC = 12 cm. What is the area of the triangle ABC?
- ABC is a triangle right angled at B. D is a point on AC such that BD is perpendicular to AC. If AB = p and BC = \sqrt{3}p, then what is BD...
- The difference between an interior angle and an exterior angle of a regular polygon is 120°. What is the number of sides of the polygon?
- An angle q is exactly one-fourth of its complementary angle. What is the value of angle q?
- The sides of a triangle are 11 cm, 60 cm and 61 cm. What is the area of the triangle formed by joining the mid-points of the sides of the tr...