Advertisements
Advertisements
प्रश्न
In the following figure, BC is a diameter of the circle and ∠BAO = 60º. Then ∠ADC is equal to ______.
विकल्प
30º
45º
60º
120º
Advertisements
उत्तर
In the following figure, BC is a diameter of the circle and ∠BAO = 60º. Then ∠ADC is equal to 60º.
Explanation:
Given: BC is a diameter of the circle and ∠BAO = 60º.
Now, in triangle OAB,
OA = OB ...[Radii of the same circle]
So, ∠ABO = ∠BAO ...[Angle opposite to equal sides are equal]
∠ABO = ∠BAO = 60º ...[Given]
Now, ∠ADC = ∠ABC = 60º ...[∠ADC and ∠ABC are angles in the same segment of a circle are equal]
Therefore, ∠ADC = 60º.
APPEARS IN
संबंधित प्रश्न
If from any point on the common chord of two intersecting circles, tangents be drawn to circles, prove that they are equal.
In the given figure, AB is a chord of length 16 cm of a circle of radius 10 cm. The tangents at A and B intersect at a point P. Find the length of PA.
In the given figure, O is the centre of the two concentric circles of radii 4 cm and 6cm respectively. AP and PB are tangents to the outer and inner circle respectively. If PA = 10cm, find the length of PB up to one place of the decimal.
PQ is a chord of length 4.8 cm of a circle of radius 3cm. The tangents at P and Q intersect at a point T as shown in the figure. Find the length of TP.
The circumference of a circle is 22 cm. The area of its quadrant (in cm2) is
In the given figure, O is the centre of the circle and ∠BDC = 42°. The measure of ∠ACB is
In the given figure, ABC is a right triangle right-angled at B such that BC = 6 cm and AB = 8 cm. Find the radius of its incircle.
Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord
In the figure, O is the centre of the circle and ∠AOB = 90°, ∠ABC = 30°. Then find ∠CAB.
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.
