Question

In the figure given above ,seg AD is perpendicular to side BC,seg BE perpendicular side AC, seg CF perpendicular to side AB. point O is orthocentre. Prove that O is incenter of triangle DEF. ((((( 10 points for correct and quick answer ))))))

Answer 1

Here is your answer.

Answer 2

Step-by-step explanation:

HINT -

on proving point F, E, C And B concyclic

we get angle 1=3 ( inscribed angle theorem)

then on proving quadrilateral OECD cyclic

we get angle 2=3 ( inscribed angle theorem)

from these

angle 1=2

seg OE is bisector of angle FED

similarly seg FO and seg DO are bisectors

therefore O is the incentre