OA and OBare the radii of a ciclewith O as centre, AOB= 1200 Tangents at A and B are - Maths - Circles

Question

OA and OBare the radii of a ciclewith O as centre, <AOB=
1200 Tangents at A and B are drawn to meet at the point
C If OCintersects the circle at the point D, then D divides OCin
the ratio ---------------

Anuradha Sharma · Accepted Answer

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_55167b00a33be%20png"
style=
"cursor: default; color: rgb(51, 51, 51); font-family: 'Arial, Verdana, sans-serif'; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; width: 296px; height: 265px;">
Given, ∠AOB = 120 degreeWe know that tangent is perpendicular to the radius at point of contact so ∠OAC=∠OBC=90 degreeSo in quadrilateral OACB, ∠ACB = 360-∠OAC-∠OBC-∠AOB=360-90-90-120=60  degreeNow in triangle OAC and OBC, OA = OB = radius OC = OC AC = BC pair of tangent from external point to circles are equal So △OAC≅△OBCHence ∠OCA=∠OCB = 30 degreeNow in right angle triangle AOC, sin 30 = OAOC=rOCOC = 2r CD = OC-OD=2r-r=rSo OD=CD = rHence D divides OC in ratio 1:1

OA and OBare the radii of a ciclewith O as centre, <AOB= 1200.Tangents at A and B are drawn to meet at the point C.If OCintersects the circle at the point D, then D divides OCin the ratio ---------------

OA and OBare the radii of a ciclewith O as centre, <AOB= 120^0.Tangents at A and B are drawn to meet at the point C.If OCintersects the circle at the point D, then D divides OCin the ratio ---------------