Answer:
AB = 21 and DE = 23
Step-by-step explanation:
Given 2 intersecting chords inside the circle then
The products of the measures of the parts of one chord is equal to the products of the measures of the parts of the other chord, that is
x(x + 13) = (x + 10)(x + 1) ← distribute parenthesis on both sides
x² + 13x = x² + 11x + 10 ← subtract x² + 11x from both sides
2x = 10 ( divide both sides by 2 )
x = 5
Hence
AB = x + 10 + x + 1 = 2x + 11 = (2 × 5) + 11 = 10 + 11 = 21
DE = x + x + 13 = 2x + 13 = (2 × 5) + 13 = 10 + 13 = 23
