ANGLES AT THE CENTER AND CIRCUMFERENCE EXAMPLES

About "Angles at the Center and Circumference Examples"

Angles at the Center and Circumference Examples :

Here we are going to see some example problems based on circles.

Angles at the Center and Circumference - Examples

Question 1 :

Find the value of x° in the following figures :

Solution :

<BOC  =  2<BAC

90 =  2x

x  =  90/2  =  45

Solution :

Equal sides will form equal angles.

<OQP  =  <QPO  =  x

<ORP  =  OPR  =  30

QPR  =  x + 30

2QPR  =  QOR

2(x + 30)  =  80

x + 30  =  80/2

x + 30  =  40

x  =  40 - 30

x  =  10

In triangle PON,

OP  =  ON  (Radius)  =  x

<ONP + <NOP + <OPN  =  180

x + 70 + x  =  180

2x  =  180 - 70

2x   =  110

x  =  110/2  =  55

Solution :

x  =  120

<BOC  =  2<BAC

<BOC + <BOA + <COA  =  360

<BOC + 140 + 100  =  360

<BOC  =  360 - 240

<BOC  =  120

<BOC  =  2 <BAC

<BAC  =  120/2  =  60

<BAC  =  60

Question 2 :

In the given figure, <CAB = 25°, find <BDC , <DBAand <COB

Solution :

In triangle APC,

<APC + <PCA + <CAP  =  180

90+ <PCA + 25  =  180

<PCA  =  180 - 115

<PCA  =  65

<DBA  =  65 (Angle in same segment)

<BDC =  25 (angle in same segment)

<COB  =  50

After having gone through the stuff given above, we hope that the students would have understood, "Angles at the Center and Circumference Examples"

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