Advertisements
Advertisements
प्रश्न
In the joining figure shown XAY is a tangent. If ∠ BDA = 44°, ∠ BXA = 36°.
Calculate: (i) ∠ BAX, (ii) ∠ DAY, (iii) ∠ DAB, (iv) ∠ BCD.
उत्तर
(i) ∠ BAX = ∠ BDA = 44° ...(Angles in the alternate segment)
(ii) ∠ ABD = ∠ BXA + ∠ BAX
∠ ABD = 36° + 44° = 80° ....(Ext. angle of a triangle = sum of internal opposite angles)
∴ ∠ DAY = ∠ ABD = 80° ...(Angles in the alternate segment)
(iii) ∠ DAB = 180° - (∠ BAX + ∠ DAY)
∠ DAB = 180° - (44° + 80°) = 56°
(v) ∠ BCD = 180° - ∠ DAB
∠ BCD = 180° - 56° = 124° ...(Opposite ∠ s of a cyclic quadrilateral are supplementary)
APPEARS IN
संबंधित प्रश्न
In the following figure; If AB = AC then prove that BQ = CQ.
In the given figure, O is the centre of the circumcircle ABC. Tangents at A and C intersect at P. Given angle AOB = 140° and angle APC = 80°; find the angle BAC.
Circles with centres P and Q intersect at points A and B as shown in the figure. CBD is a line segment and EBM is tangent to the circle, with centre Q, at point B. If the circle are congruent; show that CE = BD.
In figure , ABC is an isosceles triangle inscribed in a circle with centre O such that AB = AC = 13 cm and BC = 10 cm .Find the radius of the circle.
In the following figure, PQ and PR are tangents to the circle, with centre O. If ∠ QPR = 60° , calculate:
∠ OQR
In the following figure, PQ and PR are tangents to the circle, with centre O. If ∠ QPR = 60° , calculate:
∠ QSR
PT is a tangent to the circle at T. If ∠ ABC = 70° and ∠ ACB = 50° ; calculate : ∠ APT
In the Figure, PT is a tangent to a circle. If m(∠BTA) = 45° and m(∠PTB) = 70°. Find m(∠ABT).
A, B, and C are three points on a circle. The tangent at C meets BN produced at T. Given that ∠ ATC = 36° and ∠ ACT = 48°, calculate the angle subtended by AB at the center of the circle.
The figure shows a circle of radius 9 cm with 0 as the centre. The diameter AB produced meets the tangent PQ at P. If PA = 24 cm, find the length of tangent PQ:
