What is the arc measure of BDC in degrees when AC and BD are the diameters of circle P

The arc measure of BDC is 45°.

Step-by-step explanation:

Consider the diagram below of a circle with diameters AC and BD, which intersects at O, the center of the circle.

The diameters AC and BD bisects each other and each half represents the radius of the circle, i.e.

AO = OC = BO = OD = r

Consider the triangle ODC.

It is a right angled triangle at O and have equal sides OD and OC.

This implies that the triangle ODC is a right-angles isosceles triangle.

The base angle property of an isosceles triangle is:

For triangle ODC,

∠D = ∠C = ∠O

So, the measure of ∠D is:

∠D = 45°

Thus, the arc measure of BDC is 45°.

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step-by-step explanation: