Advertisements
Advertisements
प्रश्न
In the following figure, O is the centre of the circle, BD = OD and CD ⊥ AB. Find ∠CAB.
Advertisements
उत्तर
Given, in the figure BD = OD, CD ⊥ AB.
In ΔOBD, BD = OD ...[Given]
OD = OB ...[Both are the radius of circle]
∴ OB = OD = BD
Thus, ΔODB is an equilateral triangle.
∴ ∠BOD = ∠OBD = ∠ODB = 60°
In ΔMBC and ΔMBD,
MB = MB ...[Common side]
∠CMB = ∠BMD = 90°
And CM = MD ...[In a circle, any perpendicular drawn on a chord also bisects the chord]
∴ ΔMBC ≅ ΔMBD ...[By SAS congruence rule]
∴ ∠MBC = ∠MBD ...[By CPCT]
⇒ ∠MBC = ∠OBD = 60° ...[∵ ∠OBD = 60°]
Since, AB is a diameter of the circle.
∴ ∠ACB = 90°
In ΔACB, ∠CAB + ∠CBA + ∠ACB = 180° ...[By angle sum property of a triangle]
⇒ ∠CAB + 60° + 90° = 180°
⇒ ∠CAB = 180° – (60° + 90°) = 30°
APPEARS IN
संबंधित प्रश्न
Two circles touch each other externally at P. AB is a common tangent to the circles touching them at A and B. The value of ∠ L APB is
(A) 30°
(B) 45°
(C) 60°
(D) 90°
Write True or False. Give reason for your answer.
Line segment joining the centre to any point on the circle is a radius of the circle.
In the given figure, PO⊥QO. The tangents to the circle at P and Q intersect at a point T. Prove that PQ and OT are right bisector of each other.
PQ is a chord of length 4.8 cm of a circle of radius 3 cm. The tangents at P and Q intersect at a point T as shown in the figure. Find the length of TP.
The length of three concesutive sides of a quadrilateral circumscribing a circle are 4 cm, 5 cm, and 7 cm respectively. Determine the length of the fourth side.
In the given figure, chord EF || chord GH. Prove that, chord EG ≅ chord FH. Fill in the blanks and write the proof.
Use the figure given below to fill in the blank:
R is the _______ of the circle.
If O is the center of the circle in the figure alongside, then complete the table from the given information.
The type of arc
| Type of circular arc | Name of circular arc | Measure of circular arc |
| Minor arc | ||
| Major arc |
From the figure, identify a point in the exterior.
Is every chord of a circle also a diameter?
