equation of the circle passing through A(1,2),B(5,2)such that the angle subtended by AB at points on the circle is pi/4​

P is the midpoint P=(3,2)

Step-by-step explanation:in ΔAOB

AB  

2

=2r  

2

(5−1)  

2

+(2−2)  

2

​  

=4

2r  

2

=16

r=2  

2

​  

slopeOM×slopeOB=−1

α−3

p−2

​  

×  

5−1

2−2

​  

=−1

α−3

p−2

​  

×0=−1

AB∥x−axis

OM∥y−axis

⇒α=3

OA=r=2  

2

​  

(3,1)(1,2)=2  

2

​  

(3−1)  

2

+(p−2)  

2

=8

p=0,4

Center(3,0)

r=2  

2

​  

(x−3)  

2

+y  

2

=8

Center(3,4)

r=2  

2

​  

(x−3)  

2

+(y−4)  

2

=8

​  

this is a very good question

step-by-step explanation:

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m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°