The ratio of OC to OA is OC/ 10√2 - OC
Explanation:
Given -
AD = 4 cm
M is the midpoint of CD
Ratio of OC to OA = ?
In a square, all the interior angles are 90°
Therefore,
ΔADC, ΔABC and ΔBCM are right angled triangle
AC is the diagonal which divides ∠DAB and ∠DCB equally
If AD = 4 cm, then AB, BC and DC are also 4cm
In ΔADC,
(AC)² = (AD)² + (DC)²
(AC)² = (10)² + (10)²
AC = 10√2 cm
AC = OA + OC
OA = AC - OC
OC/OA = OC / AC - OC
OC / OA = OC / 10√2 - OC
Therefore, the ratio of OC to OA is OC/ 10√2 - OC
