On the AM side of triangle ABM, point H is marked so that AH: NM = 4: 7; Point C is the middle

| September 16, 2021 | education

On the AM side of triangle ABM, point H is marked so that AH: NM = 4: 7; Point C is the middle of side AB, point O is the middle of the segment BH, AM = 22 cm, angle BOC = 105 degrees. Find CO and angle BNM.

Let the length of the segment AH = 4 * X cm, then MH = 7 * X cm.

AH + MH = AM = 22 cm.

4 * X + 7 * X = 11 * X = 22 cm.

X = 22/11 = 2.

AH = 2 * 4 = 8 cm.

In triangle ABH, point C is the middle of AB, point O is the middle of BH, then CO is the middle line of the triangle, and then CO = AH / 2 = 8/2 = 4 cm and CO is parallel to AH.

Angle ANO = BОС = 105 as the corresponding angles at the intersection of parallel CO and AH secant BH.

The BHM angle is adjacent to the ANO angle, then the BHM angle = 180 – 105 = 75.

Answer: The length of the CO segment = 4 cm, the angle BHM = 750.



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