Question
Download Solution PDFΔABC is inscribed in a circle with centre O. If AB = 17 cm, BC = 10 cm and AC = 9 cm, find the length of AO
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF
Concept used:
Length of circumradius = (A × B × C)/(4 × Δ)
where A, B, C are the lengths of the 3 sides of the triangle
Δ → Area of the triangle.
Area of triangle = √{s(s - a)(s - b)(s - c)}
where a, b, c are the lengths of the 3 sides of the triangle
s → Semiperimeter
Calculation:
s = (a + b + c)/2
⇒ s = (10 + 9 + 17)/2
⇒ s = 18
Area of ΔABC = √{18(18 - 10)(18 - 9)(18 - 17)
⇒ √(18 × 8 × 9 × 1)
⇒ 36 cm2
Circumradius of the triangle = (a × b × c)/4Δ
⇒ (10 × 17 × 9)/(4 × 36)
⇒ 10.6 cm
∴ Circumradius of the triangle is 10.6 cm
Last updated on Jul 17, 2025
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