If two circles with radii 8 cm and 3 cm, respectively, touch internally, then find the distance between their centers.
If the sides of a triangle are 6 cm, 8 cm and 10 cm, respectively, then determine whether the triangle is a right angle triangle or not.
In the figure given below, Ray PT is bisector of ∠QPR. If PQ = 5.6 cm, QT = 4 cm and TR = 5 cm, find the value of x .
In the following figure, Q is the center of the circle. PM and PN are tangents to the circle. If ∠MPN = 40° , find ∠MQN.
Write the equation 2x - 3y - 4 = 0 in the slope intercept form. Hence, write the slope and y-intercept of the line.
If (4,-3) is a point on the line AB and slope of the line is (-2), write the equation of the line AB.
In a triangle ABC, line l || Side BC and line l intersects side AB and AC in points P and Q, respectively. Prove that: `"AP"/"BP"="AQ"/"QC"`
In figure, ΔABC is an isosceles triangle with perimeter 44 cm. The base BC is of length 12 cm. Side AB and side AC are congruent. A circle touches the three sides as shown in the figure below. Find the length of the tangent segment from A to the circle.
Draw tangents to the circle with center ‘C’ and radius 3.6 cm, from a point B at a distance of 7.2 cm from the center of the circle.
Write the equation of each of the following lines:
- The x-axis and the y-axis.
- The line passing through the origin and the point (-3, 5).
- The line passing through the point (-3, 4) and parallel to X-axis.
From the top of a lighthouse, an observer looks at a ship and finds the angle of depression to be 60° . If the height of the lighthouse is 90 meters, then find how far is that ship from the lighthouse? (√3 = 1.73)
The sum of length, breadth and height of a cuboid is 38 cm and the length of its diagonal is 22 cm. Find the total surface area of the cuboid.
In triangle ABC, ∠C=90°. Let BC= a, CA= b, AB= c and let 'p' be the length of the perpendicular from 'C' on AB, prove that:
1. cp = ab
Construct the circumcircle and incircle of an equilateral triangle ABC with side 6 cm and centre O. Find the ratio of radii of circumcircle and incircle.