Answer:
The value of x is 5
The lengths of the chords are 24 units and 42 units
Step-by-step explanation:
In a circle if two chords intersected at a point inside it there are four segments created, two in each cord, the products of the lengths of the line segments on each chord are equal
∵ BD and CE are two chords in a circle intersected at W
∴ The two segments of chord BD are BW and WD
∴ The two segments of chord CE are CW and WE
- By using the rule above
∴ BW × WD = CW × WE
∵ BW = 2x + 10 and WD = 4
∵ CW = 7x + 5 and WE = 2
- Substitute them in the rule above
∴ (2x + 10) × 4 = (7x + 5) × 2
∴ 4(2x) + 4(10) = 2(7x) + 2(5)
∴ 8x + 40 = 14x + 10
- Subtract 14x from both sides
∴ - 6x + 40 = 10
- Subtract 40 from both sides
∴ - 6x = - 30
- Divide both sides by - 6
∴ x = 5
∵ Chord BD = 2x + 10 + 4
∴ Chord BD = 2x + 14
- Substitute the value of x to find its length
∴ Chord BD = 2(5) + 14 = 10 + 14
∴ Chord BD = 24 units
∵ Chord CE = 7x + 5 + 2
∴ Chord CE = 7x + 7
- Substitute the value of x to find its length
∴ Chord CE = 7(5) + 7 = 35 + 7
∴ Chord CE = 42 units
