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
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
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.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Question : Two circles touch each other externally at any point C. PQ is the direct common tangent to both the circles touching the circles at point P and point Q. If the radii of the circles are 36 cm and 16 cm, respectively, then the length of PQ is:
Question : Two circles of radii 12 cm and 13 cm are concentric. The length of the chord of the larger circle which touches the smaller circle is:
Question : The length of the common tangent PQ for two circles touching externally is 16 cm. If the radius (OP) of the bigger circle is 20 cm, then the radius (RQ) of the smaller circle is:
Question : The radii of two concentric circles are 34 cm and 50 cm. A and D are the points on a larger circle and B and C are the points on a smaller circle. If ABCD is a straight line and BC = 32 cm, then what is the length of AD?
Question : The radius of the two concentric circles are 17 cm and 10 cm. A straight line ABCD intersects the larger circle at points A and D and intersects the smaller circle at points B and C. If BC = 12 cm, then the length of AD(in cm) is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile