The circle below has center O, and its radius is 4 ft. Given that m ZAOB=50°find the length of the minor arc AB.
1 answer:
Answer:
The length of minor arc AB is π ft
Step-by-step explanation:
The formula of the length of an arc in a circle is L = × 2πr, where α is the central angle subtended by the arc, and r is the radius of the circle
∵ The radius of the circle is 4 ft
∴ r = 4
∵ ∠AOB is a central angle subtended by minor arc AB
∵ m∠AOB = 50°
∴ α = 50°
Substitute the values of r and α in the rule above
∵ L = × 2π(4)
∴ L = π
∴ The length of minor arc AB is π ft
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Answer:
The measure of ∠G is 59°
Step-by-step explanation:
<em>When </em><em>two secants</em><em>, intersect at </em><em>a point outside a circle</em><em> then the </em><em>measure of the angle formed between them</em><em> is </em><em>one-half the positive difference of the measures of the intercepted arcs.</em>
<em></em>
In the given figure
∵ GT is a secant that intersects the circle at points H and T
∵ GE is a secant that intersects the circle at points F and E
∴ The intercepted arcs are HF and TE
∵ GT ∩ GE at G
∵ Point G is outside the circle
→ By using the rule above
∴ m∠G = (m arc TE - m arc HF)
∵ m arc TE = 175°
∵ m arc HF = 57°
→ Substitute them in the rule above
∵ m∠G = (175 - 57) =
(118)
∴ m∠G = 59
∴ The measure of ∠G is 59°