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Geometry and Mensuration: Test 22

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Question 1
AB= 8 cm and CD= 6 cm are two parallel chords on the same side of the centre of a circle. The distance between them is 1 cm. The radius of the circle is
A
5 cm
B
4 cm
C
3 cm
D
2 cm
Question 1 Explanation: 
36
$ \begin{array}{l}Let\text{ }the\text{ }radius\text{ }be\text{ }x\text{ }cm.\\\sqrt{{{x}^{2}}-9}-\sqrt{{{x}^{2}}-16}=1\\Putting\,x=5,\\L.H.S=1=R.H.S\end{array}$
Question 2
Two parallel chords are drawn in a circle of diameter 30 cm. The length of one chord is 24 cm and the distance between the two chords is 21 cm. The length of the other chord is
A
10 cm
B
18 cm
C
12 cm
D
16 cm
Question 2 Explanation: 
image-1-1
image-2-1
Question 3
Chords AB and CD of a circle intersect externally at P. If AB= 6 cm, CD= 3 cm and PD= 5 cm, then the length of PB is
A
5 cm
B
7.35 cm
C
6 cm
D
4 cm
Question 3 Explanation: 
image-3
image-4
Question 4
AB and CD are two parallel chords on the opposite sides of the circle $ \displaystyle \overline{AB}=\text{ }10\text{ }cm,\,\,\overline{CD}=\text{ }24\text{ }cm$and the radius of the circle is 13cm, the distance between the chords is
A
17 cm
B
15 cm
C
16 cm
D
18 cm
Question 4 Explanation: 
39
$ \begin{array}{l}Let\text{ }O\text{ }be\text{ }the\text{ }center\text{ }of\text{ }the\text{ }circle.\\OB=OD=13\text{ }cm\\Thus\text{ }the\text{ }distance\text{ }between\text{ }them\text{ }is\\\sqrt{{{13}^{2}}-{{5}^{2}}}+\sqrt{{{13}^{2}}-{{12}^{2}}}\\=12+5\\=17\end{array}$
Question 5
The length of the common chord of two circles of radii 15 cm and 20 cm whose centres are 25 cm apart, is (in cm)
A
12
B
24
C
36
D
48
Question 5 Explanation: 
image-5
image-6
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