Fill In The Blanks[1 Marks ]

Question 11 Mark

$\frac{3\cot40^\circ}{\tan50^\circ}-\frac{1}{2}\Big(\frac{\cos35^\circ}{\sin55^\circ}\Big)=$ ________.

Answer

$\frac{3\cot40^\circ}{\tan50^\circ}-\frac{1}{2}\Big(\frac{\cos35^\circ}{\sin55^\circ}\Big)=$ $\frac{5}{2}$ Solution: $\Rightarrow\frac{3\cot40^\circ}{\tan50^\circ}-\frac{1}{2}\Big(\frac{\cos35^\circ}{\sin55^\circ}\Big)$ $\Rightarrow\frac{3\cot(90^\circ-40^\circ)}{\tan50^\circ}-\frac{\cot35^\circ}{2\sin(90^\circ-55^\circ)}$ $\Rightarrow\frac{3\tan50^\circ}{\tan50^\circ}-\frac{\cot35^\circ}{2\cot35^\circ}$ $\Rightarrow3-\frac{1}{2}$ $\Rightarrow\frac{6-1}{2}$$\Rightarrow\frac{5}{2}$

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Question 21 Mark

The distance between two parallel tangents of a circle of radius 4cm is _________.

Answer

The distance between two parallel tangents of a circle of radius 4cm is 8cm.
Solution:

Distance between the two parallel tangent to a circle = diameter
= 2 × r
= 2 × 4
= 8cm

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Question 31 Mark

In given Fig. the length PB = _________ cm.

Answer

In given Fig. the length PB = 4cm.
Solution:
The lenght of AB = 8cm (using Pythagoras).
$\text{And}\ \text{AB}=2\text{PB}$
$\frac{\text{AB}}{2}=\text{PB}$
$\frac{8}{2}=\text{PB}$
$\text{PB}= 4\text{cm}.$

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Question 41 Mark

In Fig. $\triangle\text{ABC}$ is circumscribing a circle, the length of BC is _______cm.

Answer

In Fig. $\triangle\text{ABC}$ is circumscribing a circle, the length of BC is 10cm.
Solution:
The length of BC is 10cm.
BP = BQ = 3cm
AR = AP = 4cm
RC = AC - AR = 7cm
RC = QC = 7cm
BC = 7 + 3 = 10cm.

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Question 51 Mark

The common point of a tangent to a circle and the circle is called ________________ .

Answer

Point of contact.

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Question 61 Mark

A circle can have ________________ parallel tangents at the most.

Answer

Two.

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Question 71 Mark