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Maths-

General

Easy

Question

In the figure, AB = AC, $angle A equals 48 to the power of ring operator end exponent$ and $angle A C D equals 18 to the power of ring operator end exponent$ Then

BC > CD
BC = CD
BC < CD
cannot decide

The correct answer is: BC = CD

We should find relation between BC and CD
Given, AB = AC
$∠ A B C = ∠ A C B = x$ (Isosceles triangle property)

In $△ A B C$
$∠ A B C + ∠ A C B + ∠ A B C = 180$ (Sum of angles of triangle)
$x + x + 48 = 180$
$2 x = 132$
$x = 6 6^{\circ}$

$∠ B C A = ∠ B C D + ∠ D C B = 66$
$∠ B C D = 66 - 18$
$∠ B C D = 4 8^{\circ}$

Now, In $△ B C D$
Sum of angles of triangle = 180
$∠ B C D + ∠ B D C + ∠ D B C = 180$
$48 + ∠ B D C + 66 = 180$
$∠ B D C = 6 6^{\circ}$
Since, $∠ B D C = ∠ D B C$
hence, $B D = C D$ (Isosceles triangle property)
Thus, $△ B D C$ is an isosceles triangle.

Hence BC=CD

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