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In Figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that AD^2 = BD × CD - CBSE Class 10 - Mathematics

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Question

 In Figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that AD2 = BD × CD

Solution

In ΔDCA and ΔDAB, we have

∠DCA = ∠DAB (Each equals to 90°)

∠CDA = ∠ADB (common angle)

∴ ΔDCA ~ ΔDAB [By AA similarity criterion]

`⇒ (DC)/(DA) = (DA)/(DA)`

⇒ AD2 = BD × CD

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 6: Triangles
Ex. 6.50 | Q: 3.3 | Page no. 150
Solution In Figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that AD^2 = BD × CD Concept: Pythagoras Theorem.
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