Maths-

General

Easy

Question

# In , DA = DB = DC. Show that .

Hint:

### Using Angles opposite to the equal sides are equal . find the angles and Add using Sum of angles in triangle ABC ,Find ∠ACB = 90°

## The correct answer is: ∠ ACB = 90°

### Step 1:- Find relation between ∠ACD,∠BAC,∠ABC and ∠DCB

In Δ ACD,

As DA = DC

∠ ACD = ∠ BAC(Angles opposite to the equal sides are equal)

In Δ BCD,

As DB = DC

∠BCD = ∠ABC(Angles opposite to the equal sides are equal)

In ABC ,

∠ BAC + ∠ ABC + ∠ ACB = 180°(sum of angles in the triangle)

Substitute ∠ ACD = ∠ BAC and ∠ BCD = ∠ ABC

∠ACD + ∠ BCD + ∠ ACB = 180°

From diagram, we get ∠ ACD + ∠BCD = ∠ ACB

2 × ∠ ACB = 180° ∠ACB = 90°

In ABC ,

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