Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Olympiad workbookIOQMCircle

Let ₁ be a circle with centre O and let AB be diameter of ₁ . Let P be a point on the segment OB different from O . Suppose another circle ₂ with centre P lies in the interior of ₁ . Tangents are drawn from A and B to the circle ₂ intersecting ₁ again at A ₁ and B ₁ respectively such that A ₁ and B₁ are on the opposite sides of A B . Given that A₁ B=5, A B₁=15 and O P=10 , find the radius of ₁ .

Correct answer

20

Step-by-step solution

aligned & r₁ r+10 = 5 2 r & r₁ r-10 = 15 2 r & r-10 r+10 = 1 3 & 3 r-30=r+10 & 2 r=40 & r=20 aligned

Practice Circle on Quantrex Academy →

More from Circle

Let A B C D be a convex cyclic quadrilateral. Suppose P is a point in the plane of the quadrilateral such that the sum of its distances from the vertices of ABCD is the least. If PLet ₁ be a circle with centre O and let AB be diameter of ₁ . Let P be a point on the segment OB different from O . Suppose another circle ₂ with centre P lies in the interior of ₁A triangle A B C with A C=20 is inscribed in a circle m . A tangent t to is drawn through B . The distance of t from A is 25 and that from C is 16 . If S denotes the area of the trA light source at the point (0,16) in the coordinate plane casts light in all directions. A disc (a circle along with its interior) of radius 2 with center at (6,10) casts a shadowLet A B be a diameter of a circle and let C be a point on , different from A and B . The perpendicular from C intersects A B at D and at E( C ) . The circle with centre at C and raConsider an isosceles triangle A B C with sides B C=30, C A=A B=20 . Let D be the foot of the perpendicular from A to B C , and let M be the midpoint of A D . Let P Q be a chord ofA semicircular paper is folded along a chord such that the folded circular arc is tangent to the diameter of the semicircle. The radius of the semicircle is 4 units and the point oLet A B be a diameter of a circle and let C be a point on the segment A B such that A C: C B=6: 7 . Let D be a point on the circle such that D C is perpendicular to A B . Let D E b Full Circle list All Olympiad workbook PYQs