Question

An isosceles triangle ABC is inscribed in a
circle when AB = AC = 20 cm and BC = 24 cm.
Find the radius of the circle.​

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

let AM ⊥ BC (A-O-M)

BM = MC =1/2 BC ( perpendicular drawn from centre to chord bisects the chord)

In Δ AMB , by pythagoras theorem,

                 AB² = AM² + BM²

                  20² = AM² + 12²

                 400- 144 = AM²

                  AM²= 256

                  AM= 16 cm

OA=OB ( radii of same circle ) = x

and AM =16

∴ OM = 16- x

In Δ OMB , by pythagoras theorem,

                OB² = OM² + BM²

                  x² = ( 16-x )²  + 12²

                 x² = 256 +x² - 32x +144  [ since ( a-b )² = a² + b² - 2ab]

                {since x² is common on both side , x² would be cancelled}

               0= 256 - 32x + 144

               0= 400 - 32x

                32x = 400

                x = $\frac{400 }{ 32 }$  = $\frac{100}{8}$= $\frac{25}{2\\}$ = 12.5

                      ∴ radius = 12 .5  

                DIAGRAM ↓