Geometry Problem

Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the problem 718 details.

## Monday, January 23, 2012

### Problem 718: Intersecting Circles, Midpoint, Angle, Measurement

Labels:
angle,
arc,
intersecting circles,
measurement,
midpoint

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Extend CDO' to cut the circle O' at E.

ReplyDeleteJoin AE, BE. Let angle AEB = y

By the result of Problem 717,

y = 65 deg

But AEBD is a cyclic quadrilateral.

So x + y = 180 deg

Hence x = 115 deg

By applying the formula that angle bda=90+bca/2 therefore half of 50=25 and by adding 90 we get 90+25=115

ReplyDeletetherefore measure of angle bda =115

x

ReplyDelete= angle subtended by major arc AB of circle(O')at D

= half the ∠ subtended by arc AB of circle (O')at center O'.

= (1/2)major∠AO'B

= (1/2)(360°-minor∠AO'B)

= (1/2)[360°-(180°-∠ACB)] (∵ AO'BC is a cyclic quadrilateral)

= (1/2)(180°+∠ACB)

= (1/2)(180°+50°)

= (1/2)(230°)

= 115°

<AO'B=180-50=130

ReplyDelete<ADB=180-<AO'B/2=180-65=115