Mathematics
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
Circles
12 Likes
Answer
We know that if two tangents are drawn from an external point to a circle then, the lengths of the tangents are equal.
From figure,
PA and PD are the tangents to the circle from P.
∴ PA = PD
QB and QA are the tangents to the circle from Q.
∴ QB = QA
Hence,
⇒ PD + BQ
⇒ PA + QA
⇒ PQ.
Hence, Option 1 is the correct option.
Answered By
5 Likes
Related Questions
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°
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
4 cm
6 cm
none of these
In the adjoining figure, PA and PB are tangents at points A and B respectively to a circle with centre O. If C is a point on the circle and ∠APB = 40°, then ∠ACB is equal to
80°
70°
90°
140°
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
