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Maths-

General

Easy

Question

In triangle $A B C comma blank angle A equals 60 degree comma angle B equals 40 degree blank$ and $blank angle C equals 80 degree.$ If $P$ is the centre of the circumcircle of triangle $A B C$ with radius unity, then the radius of the circumcircle of triangle $B P C$ is

$1$
$\sqrt{3}$
$2$
$\sqrt{3} / 2$

The correct answer is: $1$

Let $R ´$ be the radius of the circumcircle of $increment A B C$ using sine rule in the triangle $B P C$
$fraction numerator a over denominator sin invisible function application 120 degree end fraction equals 2 R subscript 1 end subscript blank$ (i)
Also, $fraction numerator a over denominator sin invisible function application 60 degree end fraction equals 2 R blank open parentheses i n blank increment A B C close parentheses$
$a equals 2 R sin invisible function application 60 degree open square brackets R equals 1 blank g i v e n close square brackets$
$rightwards double arrow a equals square root of 3$

From Eq.(i), we get $blank R subscript 1 end subscript equals fraction numerator 2 square root of 3 over denominator square root of 3 end fraction cross times fraction numerator 1 over denominator 2 end fraction$

Related Questions to study

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If in $blank increment A B C comma sin invisible function application A cos invisible function application B equals fraction numerator square root of 2 minus 1 over denominator square root of 2 end fraction$ and $sin invisible function application B cos invisible function application A equals fraction numerator 1 over denominator square root of 2 end fraction comma blank$ then the triangle is

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