The radius of the circle, passing through the vertices of a right angles triangle, when the lengths of perpendicular sides are $6 c m$ and $8 c m$ , is.

10 c m

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14 c m

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7 c m

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5 c m

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Solution

The correct option is C $5 c m$
$G i v e n - A B C i s a r i g h t t r i a n g l e w i t h ∠ A B C = 90^{o} a n d a c i r c l e c i r c u m s c r i b e s Δ A B C . A B = 6 c m & B C = 8 c m . T o f i n d o u t - T h e r a d i u s o f t h e g i v e n c i r c l e = ? S o l u t i o n - I n Δ A B C, ∠ A B C = 90^{o} . S i n c e i t i s a n a n g l e i n t h e s e m i c i r c l e, t h e h y p o t e n u s e A C i s t h e d i a m e t e r o f t h e c i r c u m s c r i b i n g c i r c l e . L e t t h e c e n t r e o f t h e g i v e n c i r c l e b e O . S o O A & O C a r e r a d i i o f t h e c i r c l e . N o w, a p p l y i n g P y t h a g o r a s T h e o r e m, w e h a v e A C = \sqrt{{A B}^{2} + {B C}^{2}} = \sqrt{6^{2} + 8^{2}} c m = 10 c m . ∴ T h e r a d i u s = O A = O C = \frac{1}{2} \times A C = \frac{1}{2} \times 10 c m = 5 c m . A n s - O p t i o n D .$

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The radius of the circle, passing through the vertices of a right angles triangle, when the lengths of perpendicular sides are 6cm and 8cm, is.

The radius of the circle, passing through the vertices of a right angles triangle, when the lengths of perpendicular sides are $6 c m$ and $8 c m$ , is.