Advertisements
Advertisements
प्रश्न
In the following figure, Q is the centre of a circle and PM, PN are tangent segments to the circle. If ∠MPN = 60°, find ∠MQN.
उत्तर
Seg PM and seg PN are tangents to the circle and seg QM and seg QN are the radii from the points of contacts.
m∠PMQ = m∠PNQ = 90° ... (Tangent is perpendicular to the radius) ... (1)
The sum of the measures of the angles of a quadrilateral is 360°.
m∠MPN + m∠PMQ + m∠MQN + m∠PNQ = 360°
60° + 90° + m∠MQN + 90° = 360°
240° + m∠MQN = 360°
m∠MQN = 360° – 240° = 120° ... [From (1)]
APPEARS IN
संबंधित प्रश्न
In the following figure, Q is the centre of a circle and PM, PN are tangent segments to the circle. If ∠MPN = 50°, find ∠MQN.
If from an external point P of a circle with centre O, two tangents PQ and PR are drawn such that ∠QPR = 120°, prove that 2PQ = PO.
From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is ______.
In the given figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to ______.
In the figure, AB and CD are common tangents to two circles of unequal radii. Prove that AB = CD.
Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.
In fig. 6, l and m are two parallel tangents to a circle with centre O, touching the circle at A and B respectively. Another tangent at C intersects the line l at D and m at E. Prove that ∠DOE = 90° ?
In the given figure, PQ is a tangent to the circle at A. AB and AD are bisectors of ∠CAQ and ∠PAC. If ∠BAQ = 30°, prove that : BD is diameter of the circle.
In the given figure, AD is a diameter. O is the centre of the circle. AD is parallel to BC and ∠CBD = 32°.
Find: ∠BED
In the given figure PA = 6, PB = 4 and PC = 8. Find PD
Find the angle between two radii at the centre of the circle as shown in the figure. Lines PA and PB are tangents to the circle at other ends of the radii and ∠APR = 110°.
A tangent is drawn from a point at a distance of 17 cm of circle C(0, r) of radius 8 cm. The length of its tangent is ______
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the center O at a point Q such that OQ = 13 cm. Length PQ is ______
The angle between two tangents to a circle may be 0°.
If from an external point B of a circle with centre O, two tangents BC and BD are drawn such that ∠DBC = 120°, prove that BC + BD = BO, i.e., BO = 2BC.
In the given figure, O is the centre of circle. Find ∠AQB, given that PA and PB are tangents to the circle and ∠APB = 75°.
In the given figure, PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q meet at a point T. Find the length of TP.
In the given figure, perimeter of ΔPQR is 20 cm. Find the length of tangent PA.
PA and PB are tangents drawn to the circle with centre O as shown in the figure. Prove that ∠APB = 2∠OAB.
