Question

34. Prove that the sum of squares on the sides of a rhombus is equal to sum of squares of its diagonals.
SECTION D
V. Answer the following questions: (6 × 4 = 24)
35. Sangeeta went to a book seller’s shop and purchased 2 textbooks of IX Mathematics and 3 textbooks of
X Mathematics for Rs. 250. Her friend Meenu also bought 4 textbooks of IX Mathematics and 6
textbooks of X Mathematics of the same kind for Rs. 500. Represent this situation algebraically and
graphically.
36. ABCD is a cyclic quadrilateral. Find the angles of the cyclic quadrilateral.
37. Solve for x
12abx2
– (9a2
–8b2
) x–6ab =0
OR
If the equation (1 + m2
)x2
+ 2mcx + (c2
–a
2
) = 0 has equal roots, prove that
c
2
= a
2
(1+m2
).
38. The 8th term of an Arithmetic progression is zero. Prove that its 38th term is triple of its 18th term.

Answer 1

Answer:

□ABCD is a rhombus with O as point of intersection of diagonals.

In ΔAOB,

∠AOB=90

0

(since diagonals are perpendicular in rhombus).

By Pythagoras theorem,

AB

2

=AO

2

+OB

2

Similarly,

BC

2

=OC

2

+OB

2

,DC

2

=OD

2

+OC

2

DA

2

=DO

2

+OA

2

AB

2

+BC

2

+CD

2

+DA

2

=2(OA

2

+OB

2

+OC

2

+OD

2

=4(AO

2

+DO

2

)

Rhombus diagonal biset each other,

AO=OC,DO=OB

AC=AO+OC

AC

2

=OA

2

+OC

2

+2AO.OC=4AO

2

Similarly,

DB

2

=4OD

2

∴AC

2

+DB

2

=4(AO

2

+DO

2

)

AB

2

+BC

2

+CD

2

+DA

2

=AC

2

+DB

2

Hence Proved.