Using a ruler and a pair of compasses only (I) construct a triangle XYZ such that XY =8cm and angle YXZ =ANGLE ZYX =45 DEGREES . Locate a point P In the triangle equidistant from XY AND XZ AND YX AND YZ . Construct a circle touching the three sides of the triangle and measure it's radius

Answer 1

from P the radii of length r are perpendicular to xz, xy, and yz and all the same.
if draw it with your compass your see a certain symmetry
call the tangent point on xz Q and the one on xy S
triangle XQP is congruent to XSP and is a right triangle
the two angles at x are 22.5 degrees
so PQ = PS = 4 tan 22.5

Answer 2

Using a ruler and a pair of compasses only.
(a)construct triangle XYZ such that,|XY|=9.5cm,|YZ|=8cm=|XZ|
(i)construct the mediator of<YXZ
(ii)construct a line equidistant from X and Z.
(b)Name the the intersection of the mediator of<YXZ and line equidistant from X and Y,A.
(c)measure (i)|AX|(ii)<XZY

Answer 3

Yes