In triangle ABC, AB = AC = x, ∠ABC = and the circumradius is equal to y. Then x/y equals Option 1: Option 2: Option 3: 2 Option 4: 2

Answer: 2. Solution: We have an isosceles triangle where AB = AC = x, ABC =, and circumradius = y. Since AB = AC, the base angles are equal: ABC = ACB = So the third angle is: BAC = 180° - 2 Using the Sine Rule, for any triangle with circumradius R: a/( A) = 2R where a is the side opposite to angle A. Picking side AB = x, the angle opposite to it is ACB = . Applying the Sine Rule: x/( ) = 2y x = 2y x/y = 2

Geometry

Triangles

Medium

In triangle $ABC, AB = AC = x, ∠ABC = \theta$ and the circumradius is equal to $y$ . Then $\frac{x}{y}$ equals

$\sin \theta$

$\cos \theta$

$2 \cos \theta$

$2 \sin \theta$

✅ Correct Option: 4

We have an isosceles triangle where $AB = AC = x$ , $\angle ABC = \theta$ , and circumradius $= y$ .

Since $AB = AC$ , the base angles are equal:

$\angle ABC = \angle ACB = \theta$

So the third angle is:

$\angle BAC = 180° - 2\theta$

Using the Sine Rule, for any triangle with circumradius $R$ :

$\dfrac{a}{\sin A} = 2R$

where $a$ is the side opposite to angle $A$ .

Picking side $AB = x$ , the angle opposite to it is $\angle ACB = \theta$ .

Applying the Sine Rule:

$\dfrac{x}{\sin \theta} = 2y$

$x = 2y \sin \theta$

$\dfrac{x}{y} = 2\sin\theta$

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In triangle ABC,AB=AC=x,∠ABC=θABC, AB = AC = x, ∠ABC = \thetaABC,AB=AC=x,∠ABC=θ and the circumradius is equal to yyy. Then xy\frac{x}{y}yx​ equals

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In triangle $ABC, AB = AC = x, ∠ABC = \theta$ and the circumradius is equal to $y$ . Then $\frac{x}{y}$ equals