In Right-angled Triangle Abc in Which ∠C = 90°, If D is the Mid-point of Bc, Prove that Ab2 = 4ad2 − 3ac2. - Mathematics

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In right-angled triangle ABC in which ∠C = 90°, if D is the mid-point of BC, prove that AB2 = 4AD2 − 3AC2.

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Solution

We have,

∠C = 90° and D is the mid-point of BC

In ΔACB, by Pythagoras theorem

AB2 = AC2 + BC2

⇒ AB2 = AC2 + (2CD)2                  [D is the mid-point of BC]

AB2 = AC2 + 4CD2

⇒ AB2 = AC2 + 4(AD2 − AC2)       [In ΔACD, by Pythagoras theorem]

⇒ AB2 = AC2 + 4AD2 − 4AC2

⇒ AB2 = 4AD2 − 3AC2

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Chapter 7: Triangles - Exercise 7.7 [Page 121]

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RD Sharma Class 10 Maths
Chapter 7 Triangles
Exercise 7.7 | Q 23 | Page 121

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