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Published on: 24/08/2019
Circles
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Questions + Answers key
Take MCQ Maths Test
1.
How many tangents parallel to a secant can a circle have?
2.
In the figure given below, find \(\angle QSR.\)
3.
What is the distance between two parallel tangents of a circle of radius 7cm?
4.
What is the angle between a tangent to a circle and the radius through the point of contact? Justify your answer
5.
Find the length of the tangent drawn from a point whose distance from the centre of a circle is 35 cm.Given that radius of the circle is 7cm.
6.
A line segment drawn through the end of a radius and perpendicular to it, is a ___________to the circle.
7.
At the point of contact, angle between the tangent and the radius is is ___________
8.
If a line and a circle have no point common, then the line lies ______________
9.
The length of the tangents drawn from an external point to a circle are _____________
10.
The common point of the tangent and the circle is called
11.
The length of the tangent is the length of the segment from an external point to the point of contact.
12.
The parallelogram circumscribing a circle is a rectangle.
13.
A tangent line intersects the circle in two points.
14.
The distance between two parallel tangents drawn to a circle is equal to the diameter of the circle.
15.
The length of tangents drawn from an external point to a circle are equal.
16.
In figure, PQ = 6 cm, QR = 7cm, RS = 4 cm PS = ...........
17.
Perimeter of \(\triangle PST\) with PQ=10 cm is
18.
Rhombus can obtain, when a
19.
A circle may have
20.
A circle have
1.
2 tangents
2.
In the figure given below, find \(\angle \)QSR.
Given: PQ and PR are tangents to a circle with centre O and
\(\angle \)QPR = 50
To find: QSR
sol. \(\angle \)QOR + \(\angle \)QPR = 180°
⇒ \(\angle \)QOR + 50° = 180°
⇒ \(\angle \)QOR = 130QOR
⇒ \(\angle \)QOR = \(1\over2\) \(\angle \)QSR [Degree measure theorem]
⇒ \(\angle \)QSR = \(1\over2\) x 130° = 65°
3.
parallel tangents of a circle can be drawn only at the end points of the diameter
⇒ I1 || I2
⇒ Distance between I1 and I2 = AB = Diameter of the circle
= 2 x r = 2 x 7 cm = 14 cm
4.
900.Because radius through point of contact of tangent to a circle is perpendicular to the tangent.
5.
Let O is the centre of the circle and P is a point such that OP = 25 cm and PQ is the tangent to the circle.
OQ = radius = 7 cm
In \(\triangle\)OQP, we have \(\angle \)Q = 90°
OP2 = OQ2 + PQ2
⇒ (25)2 = 72 + PQ2 ⇒ PQ2 = 625 - 49 = 576
⇒ PQ = 24 cm
6.
( )
tangent line.
7.
( )
A right angle \(\left( { 90 }^{ \circ } \right) \).
8.
( )
outside the circle.
9.
( )
equal
10.
( )
point of contact.
11.
(a)
12.
(b)
13.
(b)
14.
(a)
15.
(a)
16.
( )
3 cm
17.
( )
20 cm
18.
( )
parallelogram circumscribing a circle
19.
( )
two parallel tangents
20.
( )
infinite tangents
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