{"id":6913,"date":"2021-10-21T22:33:23","date_gmt":"2021-10-21T17:03:23","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6913"},"modified":"2021-10-23T15:52:52","modified_gmt":"2021-10-23T10:22:52","slug":"let-c-be-the-circle-with-center-at-11-and-radius-1-if-t-is-the-circle-centered-at-0y-passing-through-origin-and-touching-the-circle-c-externally-then-the-radius-of-t-is-equal-to","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/let-c-be-the-circle-with-center-at-11-and-radius-1-if-t-is-the-circle-centered-at-0y-passing-through-origin-and-touching-the-circle-c-externally-then-the-radius-of-t-is-equal-to\/","title":{"rendered":"Let C be the circle with center at (1,1) and radius 1. If T is the circle centered at (0,y) passing through origin and touching the circle C externally, then the radius of T is equal to"},"content":{"rendered":"

Solution :<\/h2>\n

Let coordinates of the center of T be (0, k).<\/p>\n

Distance between their center is<\/p>\n

k + 1 = \\(\\sqrt{1 + (k – 1)^2}\\)<\/p>\n

where k is radius of circle T and 1 is radius of circle C,\u00a0so sum of these is distance between their centers.<\/p>\n

\\(\\implies\\) k + 1 =\u00a0 \\(\\sqrt{k^2 + 2 – 2k}\\)<\/p>\n

\\(\\implies\\) \\(k^2 + 1 + 2k\\) = \\(k^2 + 2 – 2k\\)<\/p>\n

\\(\\implies\\) k = \\(1\\over 4\\)<\/p>\n

So, the radius of circle T is k i.e. \\(1\\over 4\\)<\/p>\n

\n

Similar Questions<\/h3>\n

The equation of the circle through the points of intersection of \\(x^2 + y^2 \u2013 1\\) = 0, \\(x^2 + y^2 \u2013 2x \u2013 4y + 1\\) = 0 and touching the line x + 2y = 0, is<\/a><\/p>\n

Find the equation of circle having the lines \\(x^2\\) + 2xy + 3x + 6y = 0 as its normal and having size just sufficient to contain the circle x(x \u2013 4) + y(y \u2013 3) = 0.<\/a><\/p>\n

Find the equation of the normal to the circle \\(x^2 + y^2 \u2013 5x + 2y -48\\) = 0 at the point (5,6).<\/a><\/p>\n

If the lines 3x-4y-7=0 and 2x-3y-5=0 are two diameters of a circle of area 49\u03c0 square units, then what is the equation of the circle?<\/a><\/p>\n

The length of the diameter of the circle which touches the X-axis at the point (1,0) and passes through the point (2,3) is<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Let coordinates of the center of T be (0, k). Distance between their center is k + 1 = \\(\\sqrt{1 + (k – 1)^2}\\) where k is radius of circle T and 1 is radius of circle C,\u00a0so sum of these is distance between their centers. \\(\\implies\\) k + 1 =\u00a0 \\(\\sqrt{k^2 + …<\/p>\n

Let C be the circle with center at (1,1) and radius 1. If T is the circle centered at (0,y) passing through origin and touching the circle C externally, then the radius of T is equal to<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[45,43],"tags":[],"yoast_head":"\nLet C be the circle with center at (1,1) and radius 1. 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