Use ruler and compasses only for this question.
(i) Construct ΔABC, where AB = 3.5 cm, BC = 6cm and ∠ABC = 60°.
(ii) Construct the locus of points inside the triangle which are equidistant from BA and BC.
(iii) Construct the locus of points inside the triangle which are equidistant from B and C.
(iv) Mark the point P which is equidistant from AB, BC and also equidistant from B and C. measure and record the length of PB.
Steps of construction:
i) Draw line BC = 6 cm and an angle CBX = 60°. Cut off AB = 3.5. Join AC, triangle ABC is the required triangle.
ii) Draw perpendicular bisector of BC and bisector of angle B
iii) Bisector of angle B meets bisector of BC at P.
⟹ BP is the required length, where, PB = 3.5 cm
iv) P is the point which is equidistant from BA and BC, also equidistant from B and C.
PB = 3.6 cm
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- Theorems Based on Loci