Question

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1. Segment AD is a diameter of circle T.

If TB is 6 cm long, m∠ATE = 94°, m∠BTC = 56°, and m∠CTD = 32°, what is the length of arc CD?

[See attachment if necessary]

A. 32 cm


B. 3.35 cm


C. 1.07 cm


D. 1.67 cm


2. If m∠DAC = 31° and m∠CAB = 27°, what is the measure of arc BD?

[See 2nd attachment if necessary]

arc BD = ___°

Answer 1

1) mesure of an arc= R.Ф, where R is the radius & Ф the angle IN RADIAN

32°===>8π/45 OR 0.5585, So mes of Arc CD = 6x0.5585 = 3.35 cm


2) DAC = 31° & CAD =27° , these 2 angles being adjacent I can write that

Angle(DAC +CAB=DCB) ==>Angle DCB =(31°+27°=58°)

To remember that any vertex of an angle on the circles, its sides intercept an arc which mesure is twice the angle,

Hence since mes Angle DCB=58°, that means the ARC intercepted, namely DB has a length of 2x 58 = 116°