Let a circle C of radius 1 and closer to the origin be such that the lines passing through the point (3, 2) and parallel to the coordinate axes touch it. Then the shortest distance of the circle C from the point (5, 5) is :
- \(2\sqrt2\)
- 5
- \(4\sqrt2\)
- 4
The Correct Option is D
Solution and Explanation
Coordinates of the centre will be: \[ (2, 1) \]
Equation of circle: \[ (x - 2)^2 + (y - 1)^2 = 1 \]
\[ QC = \sqrt{(5 - 2)^2 + (5 - 1)^2} = 5 \]
Shortest distance: \[ RQ = CQ - CR = 5 - 1 = 4 \]
Top Questions on Circles
In the following figure chord MN and chord RS intersect at point D. If RD = 15, DS = 4, MD = 8, find DN by completing the following activity:
Activity :
\(\therefore\) MD \(\times\) DN = \(\boxed{\phantom{SD}}\) \(\times\) DS \(\dots\) (Theorem of internal division of chords)
\(\therefore\) \(\boxed{\phantom{8}}\) \(\times\) DN = 15 \(\times\) 4
\(\therefore\) DN = \(\frac{\boxed{\phantom{60}}}{8}\)
\(\therefore\) DN = \(\boxed{\phantom{7.5}}\)In the following figure, circle with centre D touches the sides of \(\angle\)ACB at A and B. If \(\angle\)ACB = 52\(^\circ\), find measure of \(\angle\)ADB.
- Prove that tangent segments drawn from an external point to a circle are congruent.
- \(\square\)ABCD is a rectangle. Taking AD as a diameter, a semicircle AXD is drawn which intersects the diagonal BD at X. If AB = 12 cm, AD = 9 cm, then find the values of BD and BX.
- In cyclic quadrilateral ABCD m\(\angle\)A = 100\(^\circ\), then find m\(\angle\)C.
Questions Asked in JEE Main exam
- Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be:
- JEE Main - 2025
- Speed and velocity
- Let \(E_1: \frac{x^2}{9} + \frac{y^2}{4} = 1\) be an ellipse. Ellipses \(E_i\) are constructed such that their centers and eccentricities are the same as that of \(E_1\), and the length of the minor axis of \(E_{i+1}\) is the length of the major axis of \(E_i\). If \(A_i\) is the area of the ellipse \(E_i\), then \(\frac{5}{\pi} \sum_{i=1}^{\infty} A_i\) is equal to:
- JEE Main - 2025
- Calculus
- The compound with molecular formula C\(_6\)H\(_6\), which gives only one monobromo derivative and takes up four moles of hydrogen per mole for complete hydrogenation has \(\_\_\_\_\_\)\( \pi \) electrons.
- JEE Main - 2025
- Aromaticity & chemistry of aromatic compounds
- A 400 g solid cube having an edge of length \(10\) cm floats in water. How much volume of the cube is outside the water? (Given: density of water = \(1000 { kg/m}^3\))
For $ \alpha, \beta, \gamma \in \mathbb{R} $, if $$ \lim_{x \to 0} \frac{x^2 \sin \alpha x + (\gamma - 1)e^{x^2} - 3}{\sin 2x - \beta x} = 3, $$ then $ \beta + \gamma - \alpha $ is equal to: