Question
In ∆ABC , G is the centroid , AB = 8 cm, BC= 12 cm and AC = 14 cm , find GD, where D is the mid-point of BC?
If AD is the median, then we know, AB² + AC² = 2{AD² + (BC/2)²} or 82 + 142 = 2{AD 2 + (12/2) 2 } or 64 + 196 = 2{AD 2 + 36} or 260/2 = AD 2 + 36 or 130 = AD 2 + 36 or AD 2 = 130 – 36 = 94 or AD = √94 = √94 Now G divides median in 2:1 so GD = 1/3 of AD = 1/3 of √94 = √94/3cmMore Geometry Questions
- What will be inradius of a right angle triangle whose base is 3 cm & height is 4 cm ?
- In ΔABC, PQ is parallel to BC If AP: PB= 3:4 and AQ= 6 cm, AC is equal to?
- What will be circumradius of an equilateral triangle of side 8 cm?
- If O is the orthocentre of ΔABC , if ∠ BOC = 1000 then what is the measure of ∠ BAC?
- If in a ΔABC, the external angle bisector of angle A, meets BC when extended at a point D, BD = 5cm , BC = 3 cm then what is AB:AC ?
- Two circles have radii of 18 cm and 32 cm, and they touch each other externally. What is the length of a common tangent between them?
- In the given figure, O is centre of the circle. Circle has 3 tangents. If ∠ QPR = 45 0 , then what is the value (in degrees) of ∠ QOR ?
- The perimeter of a rectangular field is 240 meters, and its length is 20% more than its breadth. What is the area of the field?
- What will be inradius of an equilateral triangle of side 10 cm?
- Length of a chord in a circle of radius 'r' cm, is 24 cm and distance between chord and centre of the circle is 35 cm. Find the value of (6r - 80).
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
