Question

*The length of a tangent drawn from a point at a distance of 10 cm of circle is 8 cm. The radius of the circle is …………*

1️⃣ 4 cm
2️⃣ 5 cm
3️⃣ 6 cm
4️⃣ 7 cm​

Answer 1

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.

Answer 2

$\huge \fbox \orange{answer}$

OP = 10cm; Radius OT = 8cm

and OT is perpendicular to PT

ln RT ie, Triangle OTP

OP²= OT²+ PT²

10² = 8² +PT²

PT² = 100-64

PT² = 36

PT = 6

therefore ur correct answer is option 3

$\huge{6}$