Question

prove that the tangent drawn from an exterior point to a circle are equal ​

Answer 1

Given

= Let,R is the external point of circle

=From R two tangent are drawn to circle. And

P and Q are point of contact.

= Let , O is the center of circle

To prove : PR= QR

Construction : I join OP , OQ and

RO

Prove

Now in ∆ PRO and ∆ QRO

a. Angle RPO = Angle RQO (by theorem radii

always perpendicular

to tangent )

b. side Po = side QO (radii of same circle)

c. side RO = side RO ( common)

so by R.H.S ∆PRQ ≅ ∆QRO

Hence by C.P.C.T RP = RQ ----- proved