Mathematics
Using ruler and compasses only, construct a rhombus ABCD whose diagonals AC and BD are 8 cm and 6 cm long respectively. Find by construction a point P equidistant from AB and AD and also equidistant from C and D. Measure PC.
Answer
Steps of construction :
Draw AC = 8 cm and BD = 6 cm as diagonals perpendicular and bisecting each other. Join the points to form rhombus ABCD.
Since, diagonals of rhombus bisects vertices, hence, AC is angular bisector of BAD.
Draw RS, the perpendicular bisector of CD.
The intersection of RS and AC is the point P which satisfies both i.e. it is equidistant from AD, AB and C and D also.
On measuring we get, CP = 3.1 cm.
Related Questions
Using ruler and compasses only, construct a ΔABC such that AB = 4.6 cm, BC = 3 cm and ∠ABC = 30°. Complete the rhombus ABDE such that C is equidistant from AB and BD. Locate the point Q on BC such that Q is equidistant from A and B.
AB and CD are two intersecting lines. Find the position of the point distant 2 cm from AB and 1.8 cm from CD.
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.
Using ruler and compasses only, construct a ΔABC in which AB = 6 cm, BC = 3.5 cm and CA = 4.6 cm.
(i) Draw the locus of a point P which moves so that it is always 3 cm from B.
(ii) Draw the locus of a point which moves so that it is equidistant from BC and CA.
(iii) Mark the point of intersection of the two loci obtained above. Measure PC.