Chapter 10, Problem 11RP

To determine

To prove : That WZ bisects $\stackrel{⌢}{XY}$ .

Explanation of Solution

Given information :

ZX and ZY are tangent at X and Y.

  

Construction :

Join XQ and YW

Formula Used :

Concept of congruence SSS Rule.

Calculation :

In $\Delta WXZ$ and $\Delta WYZ$

XW = YW     (radii)

ZX = ZY     (Tangent drawn from an exterior point to a circle are of equal length)

ZW = ZW     (common)

  $\therefore \Delta WXZ\cong \Delta WYZ$     (By SSS Rule)

  $\angle XWZ=\angle ZWY$     (By C.P.C.T.)

i.e. $\angle XWP=\angle YWP$ are the angle extended by arc $\stackrel{⌢}{XP}$ and $\stackrel{⌢}{YP}$ respectively.

Since, angle extended by arc at center are equal.

So, $\stackrel{⌢}{XP}=\stackrel{⌢}{YP}$

i.e. ZW bisects $\stackrel{⌢}{XY}$ .