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Given ab and cb are tangents of p, and m =10°. what is the measure of abp?

You are standing next to a really big circular lake. you want to measure the diameter of the lake, but you don't want to have to swim across with a measuring tape! you decide to walk around the perimeter of the lake and measure its circumference, and find that it's 400\pi\text{ m}400? m. what is the diameter dd of the lake?

Meg constructed triangle poq and then used a compass and straightedge to accurately construct line segment os, as shown in the figure below, which could be the measures of angles pos and angle poq?