CLASS-8
CIRCLE - PROBLEM & SOLUTION

Example.1) – In the adjoining figure, find AB and the radius of the circle

Ans.) An angle in a semicircle = 90⁰ => ∠ACB = 90⁰

In the right angled triangle ABC,

AB² = BC² + CA² = (12² + 16²) cm² = 400 cm²

So, AB = √400 cm² = √20²cm² = 20cm

And, the radius = ½ X AB =  ½ X 20cm =  10 cm    (Ans.)



Example.2) In the adjoining figure, find OM

Ans.)  MN is a tangent to the circle at M. so, OM ⊥ MN    

Now, in the right ∆ OMN,

OM² + MN² = ON²

So, OM = √ON²- MN²

         = √17² - 8² cm

         = √289 – 64 cm

                                             =  √225 = 15 cm   (Ans.)


Example.3)  In the figure, OA = 6.5 cm and AC = 5cm, Find = BC

Ans.)   An angle in a semicircle = 90⁰ => ∠ACB = 90⁰                   

 AB = 2 X OA

= 2 X 6.5 cm = 13 cm

In the right angles triangle ∆ ABC, AB² = AC² + BC²

=> BC = √ AB² - AC² =  √13² - 5² 

       = √169 – 25 = √144 cm = 12 cm        (Ans.)