Question

XYZ is a right angled triangle with X=90°, XY=9cm, and YZ=12cm. OX is perpendicular to YZ. Find OX​

Answer 1

Answer:

6cm

Step-by-step explanation:

ox is a perpendicular of yz.yz radius is 12cm.so' radius of ox is 6cm

Answer 2

OX would be $\dfrac{9\sqrt{7}}{4}$ units

Step-by-step explanation:

Given,

In right triangle XYZ,

X=90°, XY=9cm, and YZ=12cm

Also, O ∈YZ

Such that, OX ⊥ YZ,

We have to find : OX

In triangles XYZ and XOY,

∠YXZ ≅ ∠XOY    ( right angles ),

∠XYZ ≅ ∠XYO

BY AA similarity postulate,

$\triangle XYZ\sim \triangle OYX$

∵ Corresponding sides of similar triangles are in same proportion,

$\implies \frac{XZ}{OX}=\frac{YZ}{XY} .....(1)$

By Pythagoras theorem,

$XZ^2 = YZ^2-XY^2 = 12^2 - 9^2 = 144 - 81 = 63$

$\implies XZ = \sqrt{63}=3\sqrt{7}$

From equation (1),

$\frac{3\sqrt{7}}{OX}=\frac{12}{9}$

$27\sqrt{7}=12OX$

$\implies OX =\frac{27\sqrt{7}}{12}=\frac{9\sqrt{7}}{4}\text{ units}$

#Learn more:

A right angle triangle have angle AOB=90°, AC=BC, OA=12cm and OC=6.5 and OB is its base. Find the measure of OB.

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