English Medium कक्षा ९ - CBSE Question Bank Solutions

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A point whose distance from the centre of a circle is greater than its radius lies in ..................... of the circle.

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A continuous piece of a circle is ............... of the circle

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An arc is a ................ when its ends are the ends of a diameter.

Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that:
ar(ΔAPB) × ar(ΔCPD) = ar(ΔAPD) × ar (ΔBPC)

true or false 

A circle is a plane figure.

In the below Fig, ABC and ABD are two triangles on the base AB. If line segment CD is
bisected by AB at O, show that ar (Δ ABC) = ar (Δ ABD)

true or false 

A chord of a circle, which is twice as long is its radius is a diameter of the circle.

true or false

Sector is the region between the chord and its corresponding arc.

true or false 

The degree measure of an arc is the complement of the central angle containing the arc.

ture or false v

The degree measure of a semi-circle is 180°.

If P is any point in the interior of a parallelogram ABCD, then prove that area of the
triangle APB is less than half the area of parallelogram.

If AD is a median of a triangle ABC, then prove that triangles ADB and ADC are equal in
area. If G is the mid-point of median AD, prove that ar (Δ BGC) = 2 ar (Δ AGC).

A point D is taken on the side BC of a ΔABC such that BD = 2DC. Prove that ar(Δ ABD) =
2ar (ΔADC).

ABCD is a parallelogram whose diagonals intersect at O. If P is any point on BO, prove
that:  (1) ar (ΔADO) = ar (ΔCDO)     (2) ar (ΔABP) = ar (ΔCBP)

ABCD is a parallelogram in which BC is produced to E such that CE = BC. AE intersects
CD at F.
(i) Prove that ar (ΔADF) = ar (ΔECF)
(ii) If the area of ΔDFB = 3 cm2, find the area of ||^gm ABCD.

ABCD is a parallelogram whose diagonals AC and BD intersect at O. A line through O
intersects AB at P and DC at Q. Prove that ar (Δ POA) = ar (Δ QOC).

ABCD is a parallelogram. E is a point on BA such that BE = 2 EA and F is a point on DC
such that DF = 2 FC. Prove that AE CF is a parallelogram whose area is one third of the
area of parallelogram ABCD.

Prove that two different circles cannot intersect each other at more than two points.

Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?

Suppose You Are Given a Circle. Give a Construction to Find Its Centre.