Question : The radii of two concentric circles are 17 cm and 25 cm. A straight line PQRS intersects the larger circle at the points P and S and intersects the smaller circle at the points Q and R. If QR = 16 cm, then the length (in cm) of PS is:
Option 1: 41
Option 2: 32
Option 3: 33
Option 4: 40
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: 40
Solution : Given: OQ = radius of smaller circle = 17 cm OP = radius of bigger circle = 25 cm QR = 16 cm OD is perpendicular to QR. So, QD = RD = $\frac{16}{2}=8$ cm From ∆ OQD, OQ 2 = OD 2 + QD 2 ⇒ OD 2 = $17^2-8^2$ ⇒ OD = $\sqrt{17^2-8^2}$ $\therefore$ OD = 15 cm From ∆ OPD, OP 2 = OD 2 + PD 2 ⇒ PD 2 = $25^2-15^2$ ⇒ OD = $\sqrt{25^2-15^2}$ $\therefore$ PD = 20 cm $\therefore$ PS = 2 × PD = 2 × 20 = 40 cm Hence, the correct answer is 40.
Candidates can download this ebook to know all about SSC CGL.
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Question : Two concentric circles are of radii 10 cm and 6 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Question : If two concentric circles have radii of 5 cm and 3 cm, then the length of the chord of the larger circle that touches the smaller circle is:
Question : Two concentric circles are drawn with radii of 20 cm and 16 cm. What will be the length of a chord of the larger circle which is tangent to the smaller circle?
Question : Two concentric circles of radii 15 cm and 13 cm are given. Find the length of the chord of the larger circle which touches the smaller circle.
Question : A circle is inscribed in $\triangle $PQR touching the sides QR, PR and PQ at the points S, U and T, respectively. PQ = (QR + 5) cm, PQ = (PR + 2) cm. If the perimeter of $\triangle $PQR is 32 cm, then PR is equal to:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile