Given a circle with center O. Two chords BD and AC, which intersect in a circle at point P. It is necessary to find

| September 18, 2021 | education

Given a circle with center O. Two chords BD and AC, which intersect in a circle at point P. It is necessary to find the degree measure of the angle BPA if the degree measures of the arcs AB and CD are 48 and 36 degrees.

Let’s build the BC chord.

The inscribed angle CBD rests on the arc CD, the degree measure of which is 360, then the value of the inscribed angle CBD = 36/2 = 180.

The inscribed angle ACB rests on the arc AB, the degree measure of which is 48, then the value of the inscribed angle ACB = 48/2 = 24.

In the triangle СРB, the angle СРB = (180 – РСВ – РВС) = (180 – 24 – 18) = 138.

The desired angle BPA is adjacent to the angle CPB, the sum of which is 180, then the angle BPA = (180 – CPB) = (180 – 138) = 42.

Answer: The angle BPA is 42.



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