Question
In the given diagram, point 'O' represents the center of a circle, while AB and DE are two distinct chords within the circle. The line segment OC is perpendicular to the chord AB, and the segment OF is perpendicular to the chord DE. The length of chord AB is provided as 24 cm, and the distance CF from the center to the perpendicular intersection with chord DE is (5 + 4√5)
In the given diagram, point 'O' represents the center of a circle, while AB and DE are two distinct chords within the circle. The line segment OC is perpendicular to the chord AB, and the segment OF is perpendicular to the chord DE. The length of chord AB is provided as 24 cm, and the distance CF from the center to the perpendicular intersection with chord DE is (5 + 4√5)
cm. The radius of the circle measures 13
cm. Determine the length of chord DE.
The perpendicular from the centre of the circle to its chord, bisects the chord. So, AC = CB = (24/2) = 12 cm Similarly, DF = FE In right rAOC, using Pythagoras theorem, AO2 = AC2 + CO2 Or, 132 = 122 + CO2 So, CO2 = 169 - 144 = 25 Or, CO = √25 = 5 cm And, OF = CF - CO = 5 + 4√5 - 5 = 4√5 cm In right rDOF, using Pythagoras theorem, DO2 = DF2 + OF2 So, DF2 = 132 - (4√5)2 Or, DF2 = 169 - 80 = 89 So, DF = √89 cm DE = DF + FE = 2DF = 2√89 cm More Circle Questions
- In a circle of radius 10 cm, a chord has length 16 cm. Find the distance of the chord from the centre of the circle.
- A semicircle has a radius of 7 cm. What is the perimeter of the semicircle?
- From an external point P, a tangent PT is drawn to a circle of radius 9 cm. If OP = 15 cm, then PT is:
- In a circle, the length of a chord AB is 48 cm & radius is 25 cm. Find the distance between centre and chord.
- Find the angle subtended at the center by an arc of a sector whose area is 462 cm² and radius is 21 cm. (Use π = 22/7)
- If the angle of a sector of a circle is 300 & its radius is 7cm , find the area of this sector?
- Find the area of the sector of a circle with radius 14 cm and central angle 90°.
- A circle has radius r. A square is inscribed inside it. Area of square is 242. Find radius.
- The circumference of the circle is 154 cm while the length of the rectangle is 15 cm more than the radius of the circle. Find the perimeter of the rectangl...
- If the lengths of the diameters of two concentric circles are 16cm and 18cm respectively, then what will be the area of the region between them?
Hey! Ask a query
Please enter email id
The email must be a valid email address.
Please enter Mobile Number
Please enter valid Mobile Number
Please enter your Doubt
Think You're Ready for RBI Grade B?
RBI Grade B 2026 Phase 1 Memory Based Paper
- 200 Questions with Detailed Solutions
- Section-wise Coverage (GA, English, Quant & Reasoning)