Question : $O$ is the circumcentre of the isosceles $\triangle ABC$. Given that $AB = AC = 5$ cm and $BC = 6$ cm. The radius of the circle is:
Option 1: 3.015 cm
Option 2: 3.205 cm
Option 3: 3.025 cm
Option 4: 3.125 cm
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
Correct Answer: 3.125 cm
Solution :
The circumradius $(R)$ of a triangle,
$ R = \frac{abc}{4K} $
where $a, b$ and $c$ are the sides of the triangle and $K$ is the area of the triangle.
Given that $AB = AC = 5$ cm ($a = b = 5$ cm) and $BC = 6$ cm ($c = 6$ cm).
The area $(K)$ of the triangle using Heron's formula,
$ K = \sqrt{s(s - a)(s - b)(s - c)} $ where $s$ is the semi-perimeter of the triangle.
$ s = \frac{a + b + c}{2} $
$ s = \frac{5 + 5 + 6}{2} = 8 $ cm
$ K = \sqrt{8(8 - 5)(8 - 5)(8 - 6)} = \sqrt{8 \times 3 \times 3 \times 2} = 12 $ cm
$ R = \frac{5 \times 5 \times 6}{4 \times 12} = \frac{150}{48} = \frac{25}{8} = 3.125$ cm
Hence, the correct answer is 3.125 cm.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
Upcoming Exams
Trending Articles around SSC CGL
