AC and BC are two equal chords of a circle with diameter AB forming a ΔABC as shown in the figure. If the radius of the circle is 5 cm. find the length of the equal chords.
Given radius AO = 5 cm, then diameter AB =10 cm
∠ACB=90∘ (Angle subtended by diameter AB on circumference)
∠A=∠B (ABC is an isosceles traingle, AC = BC)
Now, angle of triangle ABC are 45∘,45∘,90∘
So, sides AC, BC, AB will be in the ratio 1:1:√
The corresponding sides can be calculated as.
(x√ = 10, ⇒ x=10√ = 5√)
So, the chord AC =CB =5√cm