Answer :

We have

** Given:** ∆AOB is a right-angled triangle, right angled at O.

AC = BC

⇒ C is the mid-point of AB.

OA = 12 cm

OC = 6.5 cm

Now the mid-point of the hypotenuse of a right triangle is equidistant from the vertices.

Therefore, AC = BC = OC

⇒ AC = BC = 6.5 cm [∵ OC = 6.5cm]

Now, AB = AC + BC [∵ C is the midpoint of AB]

⇒ AB = 6.5 + 6.5

⇒ AB = 13 cm

According to Pythagoras theorem in ∆AOB,

AO^{2} + OB^{2} = AB^{2}

⇒ OB^{2} = AB^{2} - AO^{2}

⇒ OB^{2} = 13^{2} - 12^{2}

⇒ OB^{2} = 169 - 144

⇒ OB^{2} = 25

⇒ OB = √25 = 5 cm

**Thus, OB = 5 cm.**

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