Subjects geometry

Collinear Points 84Feb5

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1. **Problem statement:** We have four collinear points A, B, C, and D arranged such that A - B - C and A - D - B. Given lengths are $AC = 84$ metres, $BC = 5$ metres, and $AD = 61$ metres. We need to find the length $DB$. 2. **Understanding the arrangement:** Since points are collinear and $A - B - C$, point B lies between A and C. Similarly, $A - D - B$ means D lies between A and B. 3. **Using segment addition:** For points on a line, the length of a segment between two points is the sum of lengths of smaller segments between intermediate points. So, $$AC = AB + BC$$ and $$AB = AD + DB$$ 4. **Calculate $AB$ using $AC$ and $BC$:** $$AB = AC - BC = 84 - 5 = 79$$ 5. **Express $DB$ using $AB$ and $AD$:** $$DB = AB - AD = 79 - 61 = 18$$ 6. **Final answer:** $$\boxed{DB = 18 \text{ metres}}$$