Please solve this!!❣️❣️
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Let radius of Circle with center Z = x
Lengths are : ZX = (2+x) cm
ZY = (9+x) cm
XY = (17) cm
In triangle XZY , By Pythagoras theorem:
Angle XZY = 90°
XZ²+ZY²=XY²
=(2+x)²+ (9+x)² = (17)²
=(4+x²+4x) + (81+x²+18x)= 289
=2x²+85+22x=289
=2x²+22x-204=0
=2(x²+11x-102)=0
By splitting the middle term:
=x²+11x-102=0
=x²+17x-6x-102=0
=x(x+17)-6(x+17)=0
=(x+17)(x-6)=0
x ≠ -17 (as radius cannot be negative)
x=6cm
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