Question 3
In Fig. 6.2, ∠BAC = 90° and AD ⊥ BC. Then,
BD . CD = BC2 (B) AB . AC = BC2
(C) BD . CD = AD2 (D) AB . AC = AD2
From Theorem 6.7,
If a perpendicular is drawn from the vertex of the right angle to
the hypotenuse then triangles on both sides of the perpendicular are similar to the whole triangle and to each other
So, ∆𝐵𝐴𝐷 ~ ∆ 𝐵𝐶𝐴
& ∆ 𝐶𝐴𝐷 ~ ∆ 𝐶𝐵𝐴
& ∆𝑩𝑨𝑫 ~ 𝜟 𝑨𝑪𝑫
Since ∆𝐵𝐴𝐷 ~ Δ 𝐴𝐶𝐷
And sides are proportional in similar triangles
𝐵𝐷/𝐴𝐷=𝐴𝐷/𝐶𝐷
BD × CD = AD2
So, the correct answer is (C)

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.