Mathematics
Without using set square or protractor, construct rhombus ABCD with sides of length 4 cm and diagonal AC of length 5 cm. Measure ∠ABC. Find the point R on AD such that RB = RC. Measure the length of AR.
Locus
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Answer
Draw AB = 4 cm as base of rhombus. From A cut an arc of 5 cm and from B cut an arc of 4 cm. Take their point of intersection as point C. From C cut an arc of 4 cm and from A also, take their point of intersection as point D. Join the points to form rhombus ABCD, and AC to form diagonal.
On measuring ∠ABC, it is equal to 78°.
We want to find a point R such that, RB = RC.
We know that locus of point equidistant from two points is the perpendicular bisector of the line segment joining them.
From figure,
PQ is the perpendicular bisector of BC and meets AD at point R, such that AR = 1.2 cm.
Hence, ∠ABC = 78° and AR = 1.2 cm.
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