It's a sin

Geometry Level 2

Given a triangle ABC, in which A B = 2 , ∠ A C B = 45 ° . AB = \sqrt{2} , \angle ACB = 45°. Determine the circumradius (radius of the circumscribed circle).


The answer is 1.

Akshat Sharda by Akshat Sharda , 21, India

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2 solutions

Akshat Sharda
Jul 8, 2015

By using the - S i n e R u l e Sine Rule A B sin ⁡ 45 ° = 2 R a d i u s \frac{AB}{\sin45°} = 2Radius

2 2 × 1 2 = R \frac{\sqrt{2}}{2× \frac{1}{\sqrt{2}}} = R

Therefore , R = 1 \boxed{R = 1}

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Akshay Yadav
Jul 8, 2015

Using the sine rule-

AB/sinC = 2R

Where R is circumradius.

(2)^0.5/sin45 = 2R

2^(0.5) * cosec45 = 2R

2^(0.5) * 2^(0.5) = 2R

2 = 2R

R = 1.

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