Question : In $\triangle X Y Z, \angle YXZ=90°$, P is a point on side YZ such that XP is perpendicular to YZ. If XP = YP = 10 cm then what will be the value of PZ?
Option 1: 8 cm
Option 2: 9 cm
Option 3: 12 cm
Option 4: 10 cm
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Correct Answer: 10 cm
Solution : In $ΔXYZ$, $\angle YXZ = 90°$ If $\angle Y = θ$, then $\angle Z = 90° - θ$ In $ΔXPY$, $\angle YPX = 90°$ [Given] ⇒ $\angle Y = \angle YXP = θ$ [As XP = PY] In $ΔXPZ$, ⇒ $\angle XPZ = 90°$ [Given] ⇒ $\angle PXZ = 90 - θ$ ⇒ $\angle Z = 90 - θ$ Since two angles are equal, $ΔXPZ$ is an isosceles triangle. ⇒ XP = PZ = 10 cm Hence, the correct answer is 10 cm.
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