Question

prove CR is bisector of PQ. If PQ and PR are the common tangents of both circles. ​

Answer 1

${\huge\star{\mathfrak{\underline{\underline{Answer:}}}}}$

$\textbf{Given :}$ Two circle with center A and B.

PQ and PR are the common tangents of both circles.

$\textbf{To Prove :}$ PR = RQ

$\textbf{Solution : }$

In circle with center A.

PR and CR are the tangents to the circle drawn from a external point R.

$\implies$PR = CR...(i)

[tangents drawn to the same circle from a point outside it are equal in lenght]

Similarly, in Circle with center B

CR = RQ ...(ii)

From equation (i) and (ii) we get.

PR = RQ

Hence, proved.

Answer 2

to find : CR bisect PQ. That is PR = RQ

Answer:

PR = CR ---<1>{Tangents from out side a point}

and

CR = RQ ----<2>

from (1),(2)

PR = RQ