Mathematics
Using ruler and compasses only, construct a ΔABC in which AB = 4 cm, BC = 5 cm and ∠ABC = 120°.
(i) Locate the point P such that ∠BAP = 90° and BP = CP.
(ii) Measure the length of BP.
Locus
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Answer
Steps of construction:
Draw AB of length 4 cm.
Make angle 120° at B, draw an arc of radius 5 cm from point B on this angle. Join BC and AC.
At point A, draw a line AE ⟂ AB.
Draw perpendicular bisector of BC
(i) Mark the point of intersection of bisector and AE as P. Thus BP = CP, as point P lies on perpendicular bisector of BC.
(ii) On measuring, BP = 6.5 cm.
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