Question

In an equilateral triangle prove that the centroid and the circumcentre of the triangle coincide

Answer 1

ॐ $\red{R}$$\orange{a}$$\green{d}$$\blue{h}$$\purple{e}$ $\red{R}$$\orange{a}$$\green{d}$$\blue{h}$$\purple{e}$ ॐ

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⎟⎟ ✪✪ CORRECT QUESTION ✪✪ ⎟⎟

Iɴ ᴀɴ ᴇϙᴜɪʟᴀᴛᴇʀᴀʟ ᴛʀɪᴀɴɢʟᴇ ᴘʀᴏᴠᴇ ᴛʜᴀᴛ ᴛʜᴇ ᴄᴇɴᴛʀᴏɪᴅ ᴀɴᴅ ᴛʜᴇ ᴄᴇɴᴛʀᴇ ᴏғ ᴛʜᴇ ᴄɪʀᴄᴜᴍᴄɪʀᴄʟᴇ (ᴄɪʀᴄᴜᴍᴄᴇɴᴛʀᴇ) ᴄᴏɪɴᴄɪᴅᴇ.

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⎟⎟ ✰✰ ＡＮＳＷＥＲ ✰✰ ⎟⎟

❂❂ Refer the image first ❂❂

From the given figure,

• BD = CD
• GD = GD (common)

★ ∠BDG = ∠CDG = 90°

★ ∆BDG ≅ ∆CDG

Hence,

★ BG = CG (C.P.C.T.)

★ CG = AG (C.PC.T.)

${\pink{\boxed{BG\:=\:CG\:=\:AG}}}$

So, G is the circumcentre of the ∆ABC.

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Answer 2

Answer:

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