Question : $ABC$ is a right-angled triangle with $\angle BAC=90°$ and $\angle ACB=60°$. What is the ratio of the circumradius of the triangle to the side $AB\ ?$
Option 1: $1:2$
Option 2: $1:\sqrt3$
Option 3: $2:\sqrt3$
Option 4: $2:3$
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $1:\sqrt3$
Solution : Given: $ABC$ is a right-angled triangle with $\angle BAC=90°$ and $\angle ACB=60°$. Let the hypotenuse $BC$ of the triangle be $2r$ units. We know, The circumradius of a right-angled triangle is half of its hypotenuse. So, the circumradius = $\frac{2r}{2}=r$ units Now, $\sin60°=\frac{AB}{BC}$ ⇒ $\frac{\sqrt3}{2}=\frac{AB}{BC}$ ⇒ $BC:AB=2:\sqrt3$ ⇒ $2r:AB=2:\sqrt3$ ⇒ $r:AB=1:\sqrt3$ Hence, the ratio of the circumradius of the triangle to the side $AB$ is $1:\sqrt3$.
Candidates can download this ebook to know all about SSC CGL.
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Question : 'O' is the circumcentre of triangle ABC lying inside the triangle, then $\angle$OBC + $\angle$BAC is equal to:
Question : In $\triangle$ABC, $\angle$B = 35°, $\angle$C = 65° and the bisector of $\angle$BAC meets BC in D. Then $\angle$ADB is:
Question : In $\triangle$ABC, if the median AD = $\frac{1}{2}$BC, then $\angle$BAC is equal to:
Question : If it is given that for two right-angled triangles $\triangle$ABC and $\triangle$DFE, $\angle$A = 25°, $\angle$E = 25°, $\angle$B = $\angle$F = 90°, and AC = ED, then which one of the following is TRUE?
Question : In the given figure, ABC is a right-angled triangle, $\angle$ABC = 90° and $\angle$ACB = 60°. If the radius of the smaller circle is 2 cm, then what is the radius (in cm) of the larger circle?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile