Question : The radii of two concentric circles are 13 cm and 8 cm. AB is the diameter of the bigger circle and BD is a tangent to the smaller circle touching it at D and the bigger circle at E. Point A is joined to D. The length of AD is:
Option 1: 20 cm
Option 2: 19 cm
Option 3: 18 cm
Option 4: 17 cm
New: SSC CHSL Tier 2 answer key released | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
Correct Answer: 19 cm
Solution :
Let the line BD intersect the bigger circle at point C.
Join AC.
OD $\perp$ BD ⇒ OD $\perp$ BC
So, BD = DC
⇒ D is the midpoint of BC.
Also, O is the midpoint of AB.
In $\triangle$BAC, O is the midpoint of AB and D is the midpoint of BC.
We know that segments joining the midpoints of any two sides of a triangle are half of the third side.
So, OD = $\frac{1}{2}$AC ⇒ AC = 2OD ⇒ AC = 2 × 8 = 16 cm
In $\triangle$OBD, OB
2
= BD
2
+ OD
2
⇒ BD
2
= $13^2-8^2$
⇒ BD = $\sqrt{105}$ = DC
In $\triangle$ADC, AD
2
= DC
2
+ AC
2
⇒ AD
2
= $(\sqrt{105})^2+16^2$
$\therefore$ AD = $\sqrt{105+256}=\sqrt{361}=19$ cm
Hence, the correct answer is 19 cm.
Related Questions
Know More about
Staff Selection Commission Combined High ...
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Get Updates Brochure
Your Staff Selection Commission Combined Higher Secondary Level Exam brochure has been successfully mailed to your registered email id “”.
Upcoming Exams
Trending Articles around SSC CHSL
