ABC is a triangle right-angled at B with sides BC = a, CA = b and AB = c. Let p be the length of the perpendicular from B to AC. Which of the following statements is/are correct?
I. p = ac/√(a² + c²)
II. pb = ac
A.I only
B.II only
C.Both I and II✓ Correct
D.Neither I nor II
Explanation
Since the triangle is right-angled at B, by Pythagoras b² = a² + c² (where b = AC is the hypotenuse). The area of the triangle = (1/2)·BC·AB = (1/2)·a·c. Also, area = (1/2)·AC·p = (1/2)·b·p. Equating: bp = ac, so II is correct. Then p = ac/b = ac/√(a² + c²), so I is also correct. Both statements are correct.
💡 Practice unlimited CDS PYQs + AI-tracked progress on each topic. Sign up free →