Advertisements
Advertisements
Question
A Rangoli has been drawn on a flor of a house. ABCD and PQRS both are in the shape of a rhombus. Find the radius of semicircle drawn on each side of rhombus ABCD.
Solution
In rhombus ABCD,
AO = OP + PA
= 2 + 2
= 4 units
And OB = OQ + QB
= 2 + 1
= 3 units
We know that, diagonals of rhombus bisect each other at 90°.
Now, In ΔOAB,
(AB)2 = (OA)2 + (OB)2 ...[By Pythagoras theorem]
⇒ (AB)2 = (4)2 + (3)2
⇒ (AB)2 = 16 + 9
⇒ (AB)2 = 25
⇒ AB = `sqrt(25)`
⇒ AB = 5 units
Since, AB is diameter of semi-circle.
∴ Radius = `"Diameter"/2`
= `(AB)/2`
= `5/2`
= 2.5 units
Hence, radius of the semi-circle is 2.5 units.
APPEARS IN
RELATED QUESTIONS
Given below is a parallelogram ABCD. Complete each statement along with the definition or property used.
(i) AD =
(ii) ∠DCB =
(iii) OC =
(iv) ∠DAB + ∠CDA =
The following figure is parallelogram. Find the degree value of the unknown x, y, z.
Can the following figure be parallelogram. Justify your answer.
In the adjacent figure HOPE is a parallelogram. Find the angle measures x,y and z. State the geometrical truths you use to find them.
If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.
Two adjacent sides of a parallelogram are 4 cm and 3 cm respectively. Find its perimeter.
Which of the following statement is true for a rhombus?
Its diagonals are equal and perpendicular.
ABCD is a rhombus. If ∠ACB = 40°, find ∠ADB.
Identify all the quadrilateral that have Four sides of equal length
In rhombus ABCD;
(i) if ∠A = 74° ; find ∠B and ∠C.
(ii) if AD = 7.5 cm ; find BC and CD.
