A, B, C, are three points on the circumference of a circle and if \(AB=AC=5\sqrt{2}\), \(\angle BAC=90^\circ\) then radius of the circle is ______.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5 cm
An angle in a semicircle is a right angle, and the other way round: if \(\angle BAC=90^\circ\) with A, B and C on the circle, then BC is a diameter.
BC \(=\sqrt{AB^2+AC^2}=\sqrt{50+50}=\sqrt{100}=10\) (Pythagoras theorem in triangle ABC)
Radius \(=\) half the diameter \(=10\div2=5\) cm