Question

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.

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Solution

Given radius AO = 5 cm, then diameter AB =10 cm In ΔACB ∠ACB=90∘ (Angle subtended by diameter AB on circumference) ∠A=∠B (ABC is an isosceles traingle, AC = BC) ∠A+∠B+90∘=180∘ x+x+90∘=180∘⇒x=45∘ Now, angle of triangle ABC are 45∘,45∘,90∘ So, sides AC, BC, AB will be in the ratio 1:1:√2 The corresponding sides can be calculated as. 45∘45∘90∘1:1:√2x:x:x√2ACCBAB↓↓↓5√25√210 (x√2 = 10, ⇒ x=10√2 = 5√2) So, the chord AC =CB =5√2cm

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