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Incircle and Its Construction

In the given ...

Question

In the given figure, O is a point in the interior of a triangle.

ABC, OD $⊥$ BC, OE $⊥$ AC and OF $⊥$ AB. Then,
$A F^{2} + B D^{2} + C E^{2} = A E^{2} + C D^{2} + B F^{2}$

T r u e

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Solution

The correct option is A $T r u e$
$A F^{2} + B D^{2} + E C^{2} = (O A^{2} - O F^{2}) + (O C^{2} - O E^{2}) + (O B^{2} - O D^{2})$

$= (O A^{2} - O E^{2}) + (O C^{2} - O D^{2}) + (O B^{2} - O F^{2})$

$= A E^{2} + C D^{2} + B F^{2} .$

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Similar questions

⊥

⊥

⊥

A F^{2} + B D^{2} + C E^{2} = A E^{2} + C D^{2} + B F^{2}

O

A B C, O D ⊥ B C, O E ⊥ A C

O F ⊥ A B

O A^{2} + O B^{2} + O C^{2} - O D^{2} - O E^{2} - O F^{2} = A F^{2} + B D^{2} + C E^{2}

A F^{2} + B D^{2} + C E^{2} = A E^{2} + C D^{2} + B F^{2}

⊥

⊥

⊥

A F^{2} + B D^{2} + C E^{2} = A E^{2} + C D^{2} + B F^{2}

A F^{2} + B D^{2} + C E^{2} = A E^{2} + C D^{2} + B F^{2}

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