Question : ABC is an isosceles triangle inscribed in a circle. If AB = AC = $12\sqrt{5}$ cm and BC = 24 cm, then the radius of circle is:
Option 1: 10 cm
Option 2: 15 cm
Option 3: 12 cm
Option 4: 14 cm
Correct Answer: 15 cm
Solution :
Given, AB = AC = 1$2\sqrt{5}$cm and BC = 24 cm
Join OB, OC, and OA.
Draw AD$\perp$ BC which will pass through centre O
OD bisects BC in D as perpendicular from the centre to a chord bisects the chord.
So, BD = CD = 12 cm
Using Pythagoras theorem in $\triangle$ ABD,
AB
2
= AD
2
+ BD
2
Or, $(12\sqrt{5})^{2}$ = AD
2
+ 12
2
Or, AD
2
= 576
Or, AD = 24 cm
Let the radius of the circle be OA = OB = OC = r
So, OD = AD – AO = 24 – r
Using Pythagoras theorem in $\triangle$ OBD,
r
2
=12
2
+ (24 – r)
2
Or, r
2
= 144 + 576 + r
2
– 48r
Or, r = 15 cm
Hence, the correct answer is 15 cm.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Result | Eligibility | Application | Selection Process | Preparation Tips | Admit Card | Answer Key
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
