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

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,

AO2 + OB2 = AB2

OB2 = AB2 - AO2

OB2 = 132 - 122

OB2 = 169 - 144

OB2 = 25

OB = √25 = 5 cm

Thus, OB = 5 cm.

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