If O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of 50 degree with PQ, then find angle POQ.
Since the tangent is perpendicular to the radius,
OPQ = 90-40=50
also, OQP=50
so, POQ=180-50-50=100
180-50-50=80
90-50=40
Now, 40-40-180=💯
Ans.👍👈👈
To find the angle POQ, we need to consider the properties of circles and tangents.
First, let's draw a diagram to visualize the situation. We have a circle with center O, a chord PQ, and a tangent PR at point P. The angle between the tangent PR and the chord PQ is given as 50 degrees.
O
/ \
P / \ Q
/ \
R______(P')
Now, let's examine the properties of tangents and chords in a circle:
1. The angle between a tangent and a chord at the point of contact is 90 degrees. In this case, angle PRQ is 90 degrees since PR is tangent to the circle.
2. The angle subtended by a chord at the center of the circle is twice the angle subtended by the same chord at any point on the circumference. In other words, angle POQ is twice angle PRQ.
Based on these properties, we can conclude that angle PRQ is 90 degrees and angle POQ is twice the angle PRQ.
Since angle PRQ is 90 degrees, angle POQ is 2 * 90 = 180 degrees.
Therefore, the angle POQ measures 180 degrees.