pls help me fast!! thank u tho
Answers
Construction :
- Draw a circle with O as centre and radius = r
- Draw a chord AB
- Draw a line OC , such that OC is perpendicular to AB ( C is mid-point of AB)
- Join OA and OB
Given :
- Distance from centre to cord (OC) = 6cm
- Length of Radius of circle = Length of chord AB - 6cm
- Length of CB = ( Length of AB)/2
To find :
Length of chord AB ( = 2x cm , let )
Solution :
As , we know that radius of circle = r cm
This gives , OA = OB = r
Also, according to question
Length of Radius of circle = Length of chord AB - 6cm
➝ r = 2x - 6. equation 1
________________________________
Now , as we know OC is perpendicular to AB
This gives OC is perpendicular to CB
Therefore ∆OBC is a right angle triangle.
Therefore by using Pythagoras theorem in ∆OBC
➝ CB² + OC² = OB²
➝ (2x/2)² + (6²) = ( r )²
Put Value of r from equation 1
➝ (x)² + 36 = (2x-6)²
➝ x² + 36 = (2x)² + (6)² - (2)(2x)(6)
➝ x² + 36 = 4x² + 36 - 24x
➝ 4x² - 24x + 36 - x² - 36 = 0
➝ (4x² - x²) - 24x + 36 - 36 = 0
➝ 3x² - 24x = 0
➝ 3x(x-8) = 0
➝ x - 8 = 0
➝ x = 8
➝ CB = 8 cm
________________________________
Now , as we know ,
Length of chord AB = 2CB
➝ Length of chord AB = 2(8 cm)
➝ Length of chord AB = 16 cm
________________________________
ANSWER : 16 cm
