Question : The diameter $PQ$ of a circle with centre $O$ is perpendicular to the chord $RS$. $PQ$ intersects $RS$ at $T$. If $RS=16$ cm and $QT=4$ cm, what is the length (in cm) of the diameter of the circle?
Option 1: 20
Option 2: 48
Option 3: 24
Option 4: 10
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: 20
Solution : Given: RS = $16$ cm QT = $4$ cm Join OR, which is a radius. Let the radius be $r$ cm. So, OT = $r-4$ cm RT = $\frac{1}{2}×RS =\frac{1}{2}×16=8$ cm From $\triangle$ ORT, $OR^2=OT^2+RT^2$ ⇒ $r^2=(r-4)^2+8^2$ ⇒ $8r=16+64$ ⇒ $8r=80$ ⇒ $r=10$ Diameter = $2r=2×10=20$ cm So, the diameter of the circle is 20 cm. Hence, the correct answer is 20.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Question : The radius of a circle is 10 cm. The distance of chord PQ from the centre is 8 cm. What is the length of chord PQ?
Question : The length of the chord of a circle is 8 cm and the perpendicular distance between the centre and the chord is 3 cm, then the diameter of the circle is equal to:
Question : In a circle, the length of a chord is 30 cm. The perpendicular distance of the chord from the centre of the circle is 8 cm. Find the diameter of the circle.
Question : The angle subtended by a chord PQ on the centre of a circle is 180°. If the length of chord PQ is 54 cm, then what will be the diameter of this circle?
Question : The distance of a chord OP from the centre of a circle is 6 cm. If the diameter of this circle is 20 cm, then what will be the sum of the radius and length of chord OP?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile