Question
AB and AC are two tangents of a circle of centre O with radius 5cm. Another tangent is drawn on the circle which intersects AB and AC at m and n respectively. Find the shortest length of mn, if the length of tangent AB is 12cm?
AO² = AB² + OB² AO² = 5² + 12² = 169 AO = 13cm Let P be the point which divides MN in two equal parts Now, In Triangle BOA and MPA ∠BAO = ∠MAP and ∠OBA = ∠MPA Therefore both the Triangles are similar, Hence AP/AB = MP/OB 8/12 = MP/5 MP = 10/3 Length of the Shortest Tangent = 2 ×10/3 = 20/3 cmMore Circle Questions
- If a wheel covers a distance of 2200 cm in 7 rotations, then the diameter of the wheel is?
- From an external point P, a tangent PT is drawn to a circle with centre O. If OP = 13 cm and radius = 5 cm, then PT is:
- In a circle AB is diameter & C is a point on circumference such that AC = 13 cm & BC = 84 cm then find the area of circle ?
- Find the area of largest square that can be inscribed in a circle of radius ‘r’.
- The circumference of a circle equals the perimeter of a square of side 14. Find area of circle.
- In a circle, two chords AB & CD are produced at P which is outside the circle . If PA= 12 cm, AB= 10 cm , PC = 2 cm then find CD.
- Find the angle subtended at the center by an arc of a sector whose area is 462 cm² and radius is 21 cm. (Use π = 22/7)
- In a circle of radius 13 cm, a chord is of length 10 cm. Find the distance of the chord from the centre.
- The wheel of a car made 300 rotations. How much distance did the car travel if the diameter of the wheel is 28 inches? (1 inch = 2.54cm)
- Two circles of radii 15 cm and 10 cm touch each other externally at a point A. PQ is the direct common tangent of those two circles of centers O ₁ and O ₂ ...
Relevant for Exams:
Hey! Ask a query
Please enter email id
The email must be a valid email address.
Please enter Mobile Number
Please enter valid Mobile Number
Please enter your Doubt
Think You're Ready for RBI Grade B?
RBI Grade B 2026 Phase 1 Memory Based Paper
- 200 Questions with Detailed Solutions
- Section-wise Coverage (GA, English, Quant & Reasoning)