Advertisements
Advertisements
Question
The bisectors of angles A and B of a scalene triangle ABC meet at O.
- What is the point O called?
- OR and OQ are drawn perpendicular to AB and CA respectively. What is the relation between OR and OQ?
- What is the relation between angle ACO and angle BCO?
Advertisements
Solution
- O is called the incentre of the incircle of ΔABC.
- OR and OQ are the radii of the incircle and OR = OQ.
- OC is the bisector of angle C.
∴ ∠ACO = ∠BCO
RELATED QUESTIONS
Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths. Give the justification of the construction.
Draw a circle with the help of a bangle. Take any point P outside the circle. Construct the pair of tangents form the point P to the circle
Draw a pair of tangents to a circle of radius 4.5 cm, which are inclined to each other at an angle of 45°.
Draw a circle of radius 4 cm and take a point Pon its circumference. Construct a tangent to the circle at P.
Draw two circles with radii 2.5 cm and 4 cm and with their centres 7 cm apart.
Draw a direct common tangent and a transverse common tangent. Calculate the length of the direct common tangent.
Draw two concentric circles with radii 4 cm and 6 cm. Taking a point on the outer circle, construct a pair of tangents to inner circle. By measuring the lengths of both the tangents, show that they are equal to each other.
Take a point O on the plane at the paper. With O as center draw a circle of radius 3 cm. Take a point P on this circle and draw a tangent at P.
Draw a circle of radius 3 cm. Construct a square about the circle.
A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the centre.
Construct a pair of tangents to a circle of radius 3 cm which are inclined to each other at an angle of 60°.
