Point O is marked in triangle ABC at height BF, such that AO = OC. The distance from point O to side AB is 4 cm

| March 9, 2021 | education

Point O is marked in triangle ABC at height BF, such that AO = OC. The distance from point O to side AB is 4 cm, and to side AC is 7 cm. Find the distance from point O to side BC.

Consider triangles AOF and COF. The angles F of triangles are straight, since OF is the height of the triangle, the sides of AO and OC are equal by condition, and the sides of OF are common.

Then right-angled triangles AOF and COF are equal in two legs.

Since AF = CF, then OF is the height, median and bisector, hence BF is the height, diagonal and bisector of ABC.

Consider triangles ВOK and  ВОМ, in which the corners of the ВKO and ВМO are straight, which means that the triangles are rectangular. The hypotenuse of the ВO is common, and the acute angles KВO and MВO are equal, since we have proved that BF is a bisector. The ВOK and ВOМ triangles are equal in hypotenuse and acute angle, therefore, OM = OK = 4 cm.

Answer: OM = 4 cm.



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