The measure of central angle LOP is 56 degrees
The measure of length LP and MP are 17 and 15 respectively
Circle geometry
In order to get the measure of LP and MP, we will use the Pythagoras theorem as shown:
LP = 2OP
LP = 2(8.5)
LP = 17
Determine the length of MP
MP² = LP² - LM²
MP² = 17² - 8²
MP² = 225
MP = 15 units
Using the SOH CAH TOA identity to get the measure of <P
Sin <P = 8/17
<P = 28.07 degrees
The angle at the center = 2(28)
The angle at the center = 56 degrees
Hene the measure of central angle LOP is 56 degrees
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