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GB-37-05-001 · Intersecting loci

Points A and B are 6 cm apart. P is equidistant from A and B and PA = 14 cm. Find the perpendicular distance from P to AB to 1 decimal place.

Intersecting Loci & Pythagoras Application of related method — Booklet p. 34
Method
1) Equidistant from A and B lies on perpendicular bisector (half-base = AB ÷
2)
2) Use Pythagoras h² = PA² − (AB/2)²
Worked Example (GB-37-05-001)
1)
P lies on the perpendicular bisector, giving half-base 3 cm.
2)
h2=142−32h^2=14^2-3^2
3)
13.7 cm
Ans = 13.7 cm