Circles Question - None

Question

From a figure with points O, P, Q, C, and M, given $OP = 5$, $OQ = 6$, $OM = \frac{5}{2}$, and $CM = 3$. Find $OC^2$ and determine the equation of a circle with centre $\left(\frac{5}{2}, 3\right)$.

Accepted Answer

Step 1: In triangle OMC, use the Pythagorean theorem.

Step 2: $OC^2 = OM^2 + MC^2$

Step 3: $OC^2 = \left(\frac{5}{2}\right)^2 + (3)^2 = \frac{25}{4} + 9 = \frac{25 + 36}{4} = \frac{61}{4}$

Step 4: Radius of the circle is $\sqrt{\frac{61}{4}} = \frac{\sqrt{61}}{2}$

Step 5: Equation of circle: $\left(x - \frac{5}{2}\right)^2 + (y - 3)^2 = \frac{61}{4}$

∴ $\lambda = \frac{61}{4}$

Question:

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