Question

From a point Q, the length of the tangent to a circle is 24 cm. and the distance of Q from the centre is 25 cm. The radius of the circle is ?

( a ) 7 cm
( b ) 12 cm
( c ) 15 cm
( d ) 24.5 cm​

Answer 1

            ༒ Qυєѕтiσи ༒

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From a point Q, the length of the tangent to a circle is 24 cm. and the distance of Q from the centre is 25 cm. The radius of the circle is ?

( a ) 7 cm

( b ) 12 cm

( c ) 15 cm

( d ) 24.5 cm

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            ★彡 Sσℓυтiσи 彡★

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۩ Refer the image first ۩

O - centre of the circle

OP - a circle radius = ?

OQ = 25 cm

PQ = 24 cm

ᴀᴘᴘʟʏɪɴɢ ᴘʏᴛʜᴀɢᴏʀᴀs ᴛʜᴇᴏʀᴇᴍ

⟹ OQ² = OP² + PQ²

⟹ 25² = OP² + 24²

⟹ OP² = 625 -576

⟹ OP² = 49

⟹ OP = √49

⟹ OP = 7

⛬ The radius of the circle is 7cm.

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Answer 2

First, draw a perpendicular from the center O of the triangle to a point P on the circle which is touching the tangent. This line will be perpendicular to the tangent of the circle.

So, OP is perpendicular to PQ i.e. OP ⊥ PQ

From the above figure, it is also seen that △OPQ is a right angled triangle.

It is given that

OQ = 25 cm and PQ = 24 cm

By using Pythagoras theorem in △OPQ,

OQ2 = OP2 +PQ2

(25)2 = OP2+(24)2

OP2 = 625-576

OP2 = 49

OP = 7 cm

So, option A i.e. 7 cm is the radius of the given circle