Question

the length of tangents from a point a at the distance of 10 cm from the centre of the circle is 8 cm find the radius of circle​

Answer 1

Answer:

Let O be the centre of circle and Let P be a point such that,

OP = 10 cm.

Let PT be the tangent such that,

PT = 6 cm.

Join OT.

Now , PT is a tangent at T and OT is the radius thorough T.

Therefore,

OT perpendicular PT.

In the right ∆OTP , we have :

OP² = OT² + PT² [ By Pythagoras theroem ]

OT = √OP² - PT²

OT = ✓(10² - (6)²

OT = √100 - 36

OT = ✓64

OT = 8 cm.

Hence,

The radius of the circle is 8 cm.

Answer 2

Step-by-step explanation:

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.