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Answer:
By comparing the ratios of sides in similar triangles ΔABC and ΔADB,we can say that
Step-by-step explanation:
Given that ∠ABC=∠ADC, AD=p and DC=q.
Let us take compare Δ ABC and Δ ADB in the attached file , ∠A is common in both triangles
and given ∠ABC=∠ADB=90°
Hence using AA postulate, ΔABC ≈ ΔADB.
Now we will equate respective side ratios in both triangles.
Since we don't know BD , BC let us take first equality and plugin the variables given in respective sides.
Cross multiply
Hence proved.
Answer:
The equation of circle is +
= 18
Step-by-step explanation:
Given the endpoints of the diameter of a circle: (-2,-3) and (4,-1)
We know that the equation of circle is
+
=
where (x,y) is any point on the circle, (h,k) is center of the circle and r is radius of circle.
To find (h,k): the center is midpoint of diameter
Midpoint of diameter with end points (x1,y1) and (x2,y2) is given by
( ,
)
( ,
)
(1,2)
Hence (h,k) is (1,2)
Substituting values of (h.k) and (x.y) as (1,2) and (4,-1) respectively in equation of circle, we get
+
=
= 18
Now substituting values of (h,k) and in equation of circle, we get
+
= 18
Hence the equation of circle is +
= 18