The required measure of the angle m∠BDC is 43°.
Given that,
In the diagram, point O is the center of the circle, and m∠ADB = 43°. If m∠AOB = m∠BOC, what is m∠BDC is to be determined.
The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²
where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.
Property of circle -
"The angle subtended by an arc of the circle to the center point of the circle is double the angle subtended by the same arc on any point the circumference of the circle."
So,
From the above property,
Angle subtended by Arc AB at center or m∠AOB is 2 * 43 = 86°
From given m∠AOB = m∠BOC,
Implies
m∠BOC = 86°
Angel subtended by arc BC at D is m∠BDC = m∠BOC /2
= 86 /2
= 43°
Thus, the required measure of the angle m∠BDC is 43°.
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