applying angle relationships to find perimeter\nwhat is the perimeter of kite obde?\n12 units\n22 units\n38…

Explanation:

Step1: Use the property of perpendicular from the center to a chord

If a line from the center of a circle is perpendicular to a chord, it bisects the chord. So, (AB = 2\times10=20) (using the Pythagorean theorem in (\triangle AOC): (OA^{2}=AC^{2}+OC^{2}), but we know that for a circle, if (OC) is perpendicular to (AB), (AC = CB). Also, in the given figure, for the kite (OBDE), we know that (OB = OE) (radii of the circle) and (BD = ED). We use the property that in a circle, if a line from the center is perpendicular to a chord, the lengths of segments can be related. For the chord - center perpendicular property: If (OA) is a radius ((OA = OB = OE)) and (OC\perp AB), (AC = CB). But for the perimeter of the kite (P=2(OB + ED)) We know that (OB) can be found using the Pythagorean theorem in (\triangle AOC) (not directly, but we can use the fact that for the chord - center perpendicular, if (AC = 10) (half of (AB) if (OC\perp AB)) and (OA) (radius) is related. But another approach: Since (OB) and (OE) are radii. Consider the right - angled triangles formed by the perpendiculars from the center to the chords. We know that (BD) and (ED) are non - radius sides of the kite. We use the fact that (OB) (radius) can be calculated using the Pythagorean theorem in (\triangle AOC) (assuming (OA) is the radius). Wait, a better way: Since (OB) is a radius. Let's use the property of the circle and right - angled triangles. We know that (OB) (radius) can be found from (\triangle AOC) (if (OA) is the radius). But actually, we can use the fact that (OB) and (OE) are equal. We know that (BD = 13) (using Pythagorean theorem: if we assume (OB) is calculated as follows: In (\triangle AOC), if (OA) is the radius. Wait, no, we can use the fact that for the kite (OBDE), (OB = OE) (radii) and (BD = ED) We know that (OB=\sqrt{10^{2}+12^{2}} = 13) (using the Pythagorean theorem in the triangle formed by the half - chord and the line from the center to the chord. Wait, no, actually, if we consider the chord (AB) with (OC\perp AB), (AC = 10) (given half - chord length if (OC) is the perpendicular from the center (O) to (AB)) and (OA) (radius) is calculated as (OA=\sqrt{10^{2}+12^{2}}=13) (assuming (OC = 12) (since (AC = 10) and (OA) is the radius). But for the kite (OBDE), (OB = 13) (radius) and (ED = 6)

Step2: Calculate the perimeter of the kite

The perimeter of a kite (P = 2(a + b)), where (a) and (b) are the lengths of two adjacent sides. Here (a=OB = 13) and (b = ED=6) (P=2(13 + 6)) (P=2\times19) (P = 38)

Answer:

38 units