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Maths-

General

Easy

Question

In the figure, $angle A O B equals 90 to the power of ring operator end exponent$ , AC = BC, OA = 12 cm and OC = 6.5 cm. Find the area of DA.OB.

15 ${c m}^{2}$
13 ${c m}^{2}$
45 ${c m}^{2}$
30 ${c m}^{2}$

The correct answer is: 30 $c m to the power of 2 end exponent$

Since mid-point of the hypotenuse of a right triangle is equidistant from the vertices. $∴ C A = C B = O C$
$\Rightarrow C A = C B = 6.5 c m$
$\Rightarrow A B = 13 c m$ In right triangle $O A B$ , we have

$A B^{2} = O B 2 + O A 2$
$\Rightarrow 1 3^{2} = O B 2 + 1 2^{2}$
$\Rightarrow O B = 5$

$∴ a r (△ A O B) = 2 1 (O A \times O B) = 2 1 (12 \times 15) = 30 c m 2$

Hence 30 is correct option

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