In an isosceles triangle MPK MP = PK = 18.MK = 9. H is located on the PK side so that HM = 9. Find PH.

univerkov | April 9, 2021 | education

By condition, НM = 9 cm, MK = 9 cm, then the KMН triangle is isosceles, then the МНК angle = MKН.

The MРK triangle is also isosceles, then the angle РMK = РCM.

In triangles MРK and KMН, the angles at the bases of MK and KН are equal, then the triangles are similar in two angles.

From the similarity of triangles: НK / KM = KM / RM.

НK = KM2 / РM = 81/18 = 4.5 cm.

Then РН = РK – НK = 18 – 4.5 = 13.5 cm.

Answer: The length of the PH segment is 13.5 cm.

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