Mathematics - Class X Question Paper - Central Board Of Secondary Education Page 32

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Q. No.
Value Points
Marks
OR
We have to find AD,
Let AC = A'C = x
∴ AB=x-h , A'B = x+h
1
Let BD = y
AB
x—h
∴
= tan α
Ü x = h + y tan α
=
1 ½
BD
y
A'B
= tan β
BD
x + h
= tan β
Ü x = y tan β — h
1
y
2h
∴ h + y tan a =y tan β — h
Ü
= y
1
tan β — tanα
BD
= cos α Ü AD = y sec α
1
AD
2h sec
AD =
½
tan β — tan α
Q23. Given, to prove, construction and correct figure
½ x 4 = 2
A
Correct proof
2
B
Draw OE || AB
½
E
O
AE
BO
In ∆ DAB, OE || AB
Ü
=
(i)
½
ED
OD
Similarly, In ∆ ADC, EO || AB || DC
AE
AO
∴
D
=
(ii)
½
C
ED
OC
BO
AO
From (i) and (ii), we get
=
½
DO
OC
Q24. Given, to prove, construction and correct figure
½x4=2
Correct proof
2
°
∠
ABCD is cyclic, therefore
D = 180° — 70° =110
½
∠
∠
∠
D=180° Ü
Also
C +
C = 180°– 110° = 70°
1
∴ ∠A = 180 — 70 = 110°
½
167

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