Math, asked by harinikadiyala, 7 months ago

what will be the length of the tangent from apoint at a distance of 8cm radius of circle is 5.​

Answers

Answered by Anonymous
2

 \huge \color{seagreen} \underline \color{seagreen} \underline \color{seagreen} \tt\star \: QUESTION \: \star

what will be the length of the tangent from apoint at a distance of 8cm radius of circle is 5.

 \huge \color{seagreen} \underline \color{seagreen} \underline \color{seagreen} \tt\star \: ANSWER\: \star

Given:- A circle with center O and AB is the tangent from point A.

Radius of circle =OB=8cm

Distance of point from the circle =AO=10cm

To find:- Length of tangent, i.e., AB=?

Solution:-

Since AB is tangent,

Therefore,

AB⊥OB[∵Tangent at any point of circle is perpendicular to the radius through point of contact]

⇒∠ABO=90°

Hence △OAB is a right angle triangle.

Using pythagoras theorem in △OAB,

AO2=AB2+OB2

(10)2=AB2+(8)2

⇒AB=100−64=6cm

Hence the length of tangent is 6cm.

Hence the correct answer is 6cm

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