Mathematics - Class X Question Paper - Central Board Of Secondary Education Page 22
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33Q22. A vertical tower is surmounted by a flagstaff of height h metres. At a point on the
ground, the angles of elevation of the bottom and top of the flagstaff are α and β
respectively. Prove that the height of lower is :
h tan α
tan β — tan α
OR
If the angle of elevation of a cloud from
a point h meters above a lake is α and
the angle of depression of its reflection
in the lake is β, prove that the distance
of the cloud from the point of observation is
2h sec α
tan β — tan α
Q23. If a line is drawn parallel to one side of a triangle, prove that the other two sides are
divided in the same ratio. Using the above result, prove the following :
The diagonals of a trapezium divide each other in the same ratio.
Q24. Prove that the sum of either pair of the opposite angles of a cyclic quadrilateral is 180°.
Using the above result, determine as under :
∠
ABCD is a cyclic trapezium with AD || BC. If
B=70°, determine the other three
angles of the trapezium.
OR
If two circles touch each other internally or externally, prove that the point of contact
lies on the line joining their centers.
Using the above result prove the following :
Two circles with centers O and O' and radii r
and r
touch each other externally at P.
1
2
AB is a line through P intersecting the two circles at A & B respectively. Prove that
OA ||OB'.
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