wiz-icon
MyQuestionIcon
MyQuestionIcon
5
You visited us 5 times! Enjoying our articles? Unlock Full Access!
Question

Construct rhombus ABCD with sides of length 5 cm and diagonal AC of length 6 cm. Find the point R on CD such that RA = RB. Then the length of CR is


A

0.5 cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

1 cm

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

1.5 cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

2 cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B

1 cm


Steps of construction:
(i) Draw a line segment AC = 6 cm.
(ii) Draw the perpendicular bisector of AC.
(iii) Draw arcs on this perpendicular from A, at a distance of 5 cm, which cuts it at B and D(as shown above).
(iv) Complete the rhombus ABCD.
(v) Draw the perpendicular bisector of AB, which intersects CD at R, such that RA = RB.
(Given, R must be such that RA = RB. i.e, point R must be equidistant from A and B. We know that the locus of a point which is equidistant from two fixed points is the perpendicular bisector of the line segment joining the two fixed points. So, we draw the perpendicular bisector of AB so as to get the locus of the point which is equidistant from A and B).

From these constructions, we see that, length of AR is 1 cm.


flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Construction of Special Quadrilaterals
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon