Constructions Test

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Constructions Test - 9

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Question 1
1 / -0

To draw tangents to a circle of radius ‘p’ from a point on the concentric circle of radius ‘q’, the first step is to find

A
mid point of q

B
mid point of p

C
mid point of p + q

D
mid point of q – r

Solution

To draw tangents to a circle of radius ‘p’ from a point on the concentric circle of radius ‘q’, the first step is to find midpoint of q.
Question 2
1 / -0

To draw a tangent at point B to the circumcircle of an isosceles right ΔABC right angled at B, we need to draw through B

A
a line parallel to AC

B
a line perpendicular to BC

C
a line inclined to 60^∘ to AB

D
a line perpendicular to AB

Solution

To draw a tangent at point B to the circumcircle of an isosceles right ΔABC right angled at B, we need to draw through B in parallel to AC.
Question 3
1 / -0

A pair of tangents can be constructed to a circle inclined at an angle of :

A
195^∘

B
185^∘

C
175^∘

D
205^∘

Solution

If the angle between the pair of tangents is always greater than 0 or less than 180°, then we can construct a pair of tangents to a circle. Hence, we can draw a pair of tangents to a circle inclined at an angle of 175°
Question 4
1 / -0

A pair of tangents can be constructed to a circle from an external point, which are inclined each other at an angle θ such that :

A
0 < θ < 180^o

B
90^o < θ < 270^o

C
180^o< θ < 360^o

D
0 < θ < 360^o

Solution

Pair of tangents and pair of radii will construct a quadrilateral to a circle and angle between radii and tangent will be 90degree and there will be two right angle. So, A pair of tangents can be constructed to a circle from an external point, which are inclined each other at an angle θθ such that 0 < θ < 180^∘.
Question 5
1 / -0

Two distinct tangents can be constructed from a point P to a circle of radius 2r situated at a distance:

A
more than 2r from the centre

B
less than 2r from the centre

C
r from the centre

D
2r from the centre

Solution

If we have to draw the tangents from an external point of the circle, then the distance of the external point from the centre should be more than the radius of the circle.
Therefore, two distinct tangents can be constructed from a point P to a circle of radius situated 2r at a distance more than from 2r the centre.

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Constructions Test - 9

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Constructions Test - 9

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Question 1

mid point of q

mid point of p

mid point of p + q

mid point of q – r

Solution

Question 2

a line parallel to AC

a line perpendicular to BC

a line inclined to 60∘ to AB

a line perpendicular to AB

Solution

Question 3

195∘

185∘

175∘

205∘

Solution

Question 4

0 < θ < 180o

90o < θ < 270o

180o < θ < 360o

0 < θ < 360o

Solution

Question 5

more than 2r from the centre

less than 2r from the centre

r from the centre

2r from the centre

Solution

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a line inclined to 60^∘ to AB

195^∘

185^∘

175^∘

205^∘

0 < θ < 180^o

90^o < θ < 270^o

180^o< θ < 360^o

0 < θ < 360^o