Question
Download Solution PDFAn isosceles ΔMNP is inscribed in a circle. If MN = MP =
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
MN = MP = 16√5 cm
NP = 32 cm
Formula used:
Area of a triangle = (1/2) × Base × Height
Circumradius = ABC/4Δ
Where. A, B, and C are three sides of the triangle
Δ = Area of the triangle
Calculation:
MD is perpendicular to NP
So, ND = DP = 32/2 = 16 cm
MD = √[(16√5)2 - (16)2] = √(1280 - 256) = √1024 = 32 cm
Area of ΔMNP = (1/2) × 32 × 32 = 512 cm2
Circumradius = (16√5 × 16√5 × 32)/(4 × 512) = 20 cm
∴ The radius (in cm) of the circle is 20 cm
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