Advertisements
Advertisements
प्रश्न
In a cyclic quadrilateral ABCD if AB || CD and ∠B = 70°, find the remaining angles.
Advertisements
उत्तर
It is given that, ABCD is a cyclic quadrilateral such that AB || CD and `angle B = 70°`
Sum of pair of opposite angles of cyclic quadrilateral is 180°.
`angle B + angle D = 180°` (`angleB = 70° ` given)
So, `angle D = 110°`
Also AB || CD and BC transversal
So,
`angleB + angleC = 180°`
`angleC = 180 ° - 70° `
= 110°
Now
`angleA + angleC = 180°`
`angleA = 180 °- angleC `
= 180° - 110 °
= 70°
`angleD` = 180° - 70°
`angleD = 110°`
APPEARS IN
संबंधित प्रश्न
Two tangent segments PA and PB are drawn to a circle with center O such that ∠APB = 120°. Prove that OP = 2AP
In fig.. O is the center of the circle and BCD is tangent to it at C. Prove that ∠BAC +
∠ACD = 90°
In the given figure, O is the centre of the circle. If ∠AOB = 140° and ∠OAC = 50°; find:
- ∠ACB,
- ∠OBC,
- ∠OAB,
- ∠CBA.
A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, find the perimeter of the ∆ABC.
The point of concurrence of all angle bisectors of a triangle is called the ______.
Suppose you are given a circle. Describe a method by which you can find the center of this circle.
In the given figure, AB is the diameter of the circle. Find the value of ∠ACD.
The length of the tangent from point A to a circle, of radius 3 cm, is 4 cm. The distance of A from the centre of the circle is ______
Let s denote the semi-perimeter of a triangle ABC in which BC = a, CA = b, AB = c. If a circle touches the sides BC, CA, AB at D, E, F, respectively, prove that BD = s – b.
What is the name for the perimeter of a circle?
