Two circles touch internally at x the smaller circle passing through the centre of larger if the straight line through x cuts the smaller circle at u and the larger at z , prove that XY=YZ
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XY = YZ if Two circles touch internally at X , the smaller circle passing through the centre of larger if the straight line through X cuts the smaller circle at Y and the larger at Z
Step-by-step explanation:
smaller circle passing through the centre of larger - Let say O
hence OX will be diameter of circle
Let join OY
now OX is diameter hence
∠OYX = (1/2)180° = 90°
XYZ is a straight line
=> ∠OYX + ∠OYZ = 180°
=> 90° + ∠OYZ = 180°
=> ∠OYZ = 90°
OX = OZ = ( radius of Larger Circle)
Now comparing Δ OXY & ΔOZY
OX = OZ ( Radius)
OY = OY (common)
∠OYX = ∠OYZ = 90°
=> Δ OXY ≅ ΔOZY
=> XY = YZ
QED
Proved
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