Let and be two distinct points on a circle with center . Let be the origin and be perpendicular to both and . If the area of the triangle is , t hen the value of is:

24 Explanation: Solution Step 1: Distance nikaalein Origin aur center ke beech ki doori: Step 2: Radius ( ) nikaalein Diya gaya hai ki , isliye ek right-angled triangle hai. Step 3: Perpendicular ki condition apply karein Kyunki , vectors ka dot product zero hoga: Yahi same condition ke liye bhi hogi: Step 4: ki value nikaalein Point circle par hai, isliye: Step 3 se value rakhne par: Isi tarah ke liye bhi aayega. Final Calculation: Sahi Option: (A) 24

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

Let $P(a_1, b_1)$ and $Q(a_2, b_2)$ be two distinct points on a circle with center $C(\sqrt{2}, \sqrt{3})$ . Let $O$ be the origin and $OC$ be perpendicular to both $CP$ and $CQ$ . If the area of the triangle $OCP$ is $\frac{\sqrt{35}}{2}$ , then the value of $a_1^2 + a_2^2 + b_1^2 + b_2^2$ is:

JEE 2023 — Mathematics PYQ

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