Question

AB is a chord of a circle at a distance 5 cm from the centre. If the length of the chord is 24 cm then the radius is ?​

Answer 1

$\Large{\underline{\underline{\bf{GivEn:-}}}}$

• OC = 5 cm
• AB = 24 cm

$\Large{\underline{\underline{\bf{To \: FiNd:-}}}}$

• What is the length of AO ?

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

☞ We have given that, the length of AB is 24 cm

• AB = 2AC

✦ AC is half of AB

✦ Length of AC is 12 cm

In triangle OAC,

• AC = 12 cm
• OC = 5 cm
• AO = x cm

Applying Pythagoras theorem in triangle AOC, we get

➸ (AO)² = (OC)² + (AC)²

➸ (x)² = (5)² + (12)²

➸ x² = 25 + 144

➸ x² = 169

➸ x = $\sf{\sqrt{169}}$

❮ x = 13 cm ❯

❝ Hence, the length of AO is 13 cm ❞

______________________

Answer 2

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