Question
Two chords of a circle 'PQ' and 'RS' crosses each other at an exterior point 'O'. Determine the length of the chord 'RS' if the chord PQ is 36 cm long, the chords 'QO' and 'SO' are 12 cm and 8 cm long, respectively.Â
Solution
ATQ, 
QO = 12 cm, SO = 8 cm, and PQ = 36 cm From the secant theorem: PO × QO = RO × SO .... (I) PO = PQ + QO = 36 + 12 = 48 cm Put the value of PO in equation (I) , we get, 48 × 12 = RO × 8 Or, RO = 48 × 12 × (1/8) So, RO = 72 cm Therefore, the length of the chord RS = RO - SO = 72 - 8 = 64 cm
More Circle Questions
- If the angle of a sector of a circle is 600 & its radius is 14 cm , find the length of arc of this sector?
- A sector of a circle has a central angle of 60°. If the radius of the circle is 14 cm, what is the area of the sector?
- Sum of diameter and circumference of a circle is 232 cm, the find area of circle.
- A metal wire when bent in the form of a square encloses an area 1089 cm 2 , if the same wire is bent in the form of a circle, then its area is?
- What is the area of a circle whose radius is equal to the length of a cube’s edge, if the cube's total surface area is 1,944 cm²? (Take π = 3)
- A circle has radius r. A square is inscribed inside it. Area of square is 242. Find radius.
- In a circle AB is diameter & C is a point on circumference such that AC = 13 cm & BC = 84 cm then find the area of circle ?
- 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 perpen...
- If the numerical value of the area of a circle is seven times that of its circumference, determine the diameter.
- A circle touches all four sides of a quadrilateral. If AB = 18 cm, BC = 21 cm, and AD = 15 cm, then what is the length of CD?
