Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

D is the mid point of side BC and AE ⊥ BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that b2 = p2+ax+a24 - Mathematics

Sum

D is the mid point of side BC and AE ⊥ BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that b2 = "p"^2 + "a"x + "a"^2/4

Solution

Given ∠AED = 90°

ED = x, DC = "a"/2    ...(D is the mid point of BC)

∴ EC = x + "a"/2, BE = "a"/2 - x

∴ In the right ∆AED

AD2 = AE2 + ED2

p2 = h2 + x2

In the right ∆AEC,

AC2 = AE2 + EC

b2 = "h"^2 + (x + "a"/2)^2

= "h"^2 + x^2 + "a"^2/4 + 2 xx x xx "a"/2

b2 = "p"^2 + "a"^2/4 + "a"x

b2 = "p"^2 + "a"x + 1/4 "a"^2

Concept: Similarity
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APPEARS IN

Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board
Chapter 4 Geometry
Unit Exercise – 4 | Q 6. (i) | Page 201