ABC is a triangle in which AB = AC and D is any point on BC. Which of the following statements is/are correct? I. AB^2 - AD^2 = CD x BD II. BC^2 + BD^2 - DC^2 = 2 BD x BC Select the answer using the code given below:

CDS 2026 PYQ with Answer — ABC is a triangle in which AB = AC and D is any point on BC. Which of…

2026 · Q48

ABC is a triangle in which AB = AC and D is any point on BC. Which of the following statements is/are correct?

IAB^2 - AD^2 = CD x BD
IIBC^2 + BD^2 - DC^2 = 2 BD x BC Select the answer using the code given below:

Elementary MathematicsGeometry: Lines, Angles and Triangles

AI only
BII only
CBoth I and II
DNeither I nor II

Explanation

By Stewart's theorem applied to the isosceles triangle (AB=AC) with D on BC: AB²=AD²+BD·DC, so I is correct. For II, writing BC=BD+DC gives BC²+BD²−DC²=2BD(BD+DC)=2BD·BC, so II is correct. Both are correct, option C.