Question

The lengths of the tangents drawn to a circle from a point outside it

A. are unequal
B. are equal

C. are equal to radius of the circle
D. are equal to diameter of the circle​

Answer 1

c is the correct answer may be its help you

Answer 2

Given :  The lengths of the tangents drawn to a circle from a point outside it

To Find : Correct option

A. are unequal

B. are equal

C. are equal to radius of the circle

D. are equal to diameter of the circle​

Solution:

 The lengths of the tangents drawn to a circle from a point outside it are equal

Let say A circle with center O  , radius  R

and Point P outside

PA and PB tangent drawn to circle

ΔPAO  and Δ PBO

PO = PO    Common

AO  = BO   = R   ( Radius)

∠PAO  = ∠ PBO  = 90°    Tangent

Hence ΔPAO ≅ Δ PBO   (RHS rule)

=> PA ≅ PB     by CPCT

=> length of PA = length of PB

Hence

The lengths of the tangents drawn to a circle from a point outside it are equal

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