In the diagram below, an and bc are tangent to o. What is the measure of adc
2 answers:
Answer:
mADC = 220°
Step-by-step explanation:
In the given diagram AB and BC are tangents to the given circle O. We have to find the measure of arc ADC.
By theorem of tangents and arcs.
m∠ABC = [m ADC- m AC ]
Since it is given in the question
∠ABC = 40 & AC = 140°
Therefore, 40 = [ m ADC - 140 ]
40 × 2 = m ADC - 140
80 + 140 = m ADC
mADC = 220°
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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°
