Mathematics
In the adjoining figure, PQR is a tangent at Q to a circle. If AB is a chord parallel to PR and ∠BQR = 70°, then ∠AQB is equal to
20°
40°
35°
45°
Answer
From figure,
BQ is chord and PQR is a tangent.
∠BQR = ∠A (∵ angles in alternate segment are equal.)
As AB || PQR
∠BQR = ∠B (∵ alternate angles are equal)
∴ ∠A = ∠B = 70°
We know that sum of angles in a triangle = 180°.
In △AQB,
⇒ ∠A + ∠B + ∠AQB = 180°
⇒ 70° + 70° + ∠AQB = 180°
⇒ 140° + ∠AQB = 180°
⇒ ∠AQB = 180° - 140°
⇒ ∠AQB = 40°.
Hence, Option 2 is the correct option.
Related Questions
In the adjoining figure, two circles touch each other at A. BC and AP are common tangents to these circles. If BP = 3.8 cm, then the length of BC is equal to
7.6 cm
1.9 cm
11.4 cm
5.7 cm
In the adjoining figure, if sides PQ, QR, RS and SP of a quadrilateral PQRS touch a circle at points A, B, C and D respectively, then PD + BQ is equal to
PQ
QR
PS
SR
Two chords AB and CD of a circle intersect externally at a point P. If PC = 15 cm, CD = 7 cm and AP = 12 cm, then AB is
2 cm
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none of these
In the adjoining figure, O is the centre of the circle. If QR = OP and ∠ORP = 20°, find the value of 'x' giving reasons.
