Question

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

Answer 1

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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