Question

what is the perimeter of kite acbo? 31 units 56 units 62 units 64 units

Explanation:

Step1: Recall properties of a kite and tangents

A kite has two pairs of adjacent sides equal. Also, tangents from a common external point to a circle are equal. So, \( AC = BC \) and \( OA = OB \) (radii of the circle, \( OA = OB = 7 \)).

Step2: Find the length of \( AC \) (and \( BC \))

We know \( OC = 25 \) and \( OA = 7 \). Using the Pythagorean theorem in triangle \( OAC \) (right triangle, since tangent is perpendicular to radius), \( AC=\sqrt{OC^{2}-OA^{2}}=\sqrt{25^{2}-7^{2}}=\sqrt{625 - 49}=\sqrt{576}=24 \). So \( AC = BC = 24 \).

Step3: Calculate the perimeter of kite \( ACBO \)

Perimeter \( = OA + OB + AC + BC \). Substituting the values: \( 7 + 7 + 24 + 24 = 62 \).

Answer:

62 units