The value of the length of DP in the diagram where P is the circumcenter of the triangle is: 15 units.
What is the Circumcenter of a Triangle?
The circumcenter is the point in the triangle where the perpendicular bisectors of the sides of the triangle intersect.
In the triangle given where P is the circumcenter, we have:
AD = DB
Substitute
2x + 14 = 8x - 52
2x - 8x = -14 - 52
-6x = -66
x = 11
AD = 2x + 14
Plug in the value of x
AD = 2(11) + 14
AD = 36
Also, AP = BP = CP = 39
AP = 39
Considering right triangle, ADP, to find DP, apply the Pythagorean theorem:
DP = √(AP² - AD²)
DP = √(39² - 36²)
DP = 15 units.
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