Write True or False and give reasons for your answer in the following:
A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the center.

True

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False

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Ambiguous

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Data Insufficient

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Solution

The correct option is B False
$P i s a p o i n t f r o m w h i c h a t a n g e n t i s t o b e d r a w n t o t h e c i r c l e w i t h c e n t r e O . ∴ P m u s t b e o u t s i d e t h e c i r c l e . N o w O P i n t e r s e c t s t h e c i r c l e a t R . ∴ O R = 3.5 c m (g i v e n) A g a i n O P = O R + R P = 3.5 c m + R P . ∴ O P > 3.5 c m . B u t g i v e n t h a t O P = 3 c m ∴ T h e s t a t e m e n t t h a t a t a n g e n t c a n b e c o n s t r u c t e d t o t h e c i r c l e f r o m P i s f a l s e . A n s - F a l s e .$

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Similar questions

A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the centre.

A pair of tangents can be constructed from a point P at a distance of 3 cm from the centre of a circle whose radius is 3.5 cm.

Question 3
State whether the following is true or false.
A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the centre.
[Thinking process
Let r = radius of circle and d = distance of a point from the centre.
1. If r = d, then point lie on the circle i.e only one tangent is possible
2. If r < d, then point lie outside the circle. i.e a pair of tangent is possible.
3. If r>d, then point lie inside the circle i.e no tangent is possible.
]

Q. Construct a pair of tangents to a cricle of radius 3.5 cm from a point 3.5 cm away from the circle.

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Write True or False and give reasons for your answer in the following:A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the center.

The correct option is B FalsePisapointfromwhichatangentistobedrawntothecirclewithcentreO.∴Pmustbeoutsidethecircle.NowOPintersectsthecircleatR.∴OR=3.5cm(given)AgainOP=OR+RP=3.5cm+RP.∴OP>3.5cm.ButgiventhatOP=3cm∴ThestatementthatatangentcanbeconstructedtothecirclefromPisfalse.Ans−False.

Write True or False and give reasons for your answer in the following:
A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the center.