Mathematics
In the figure, two circles touch each other at X. YZ and PX are common tangents to these circles. If YP = 3.8 cm, then YZ = ?
1.9 cm
11.4 cm
7.6 cm
7 cm
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,
PX and PY are the tangents to the first circle.
∴ PX = PY = 3.8 cm
PX and PZ are tangents to the second circle.
∴ PZ = PX = 3.8 cm
From figure,
YZ = PZ + PY = 3.8 + 3.8 = 7.6 cm.
Hence, option 3 is the correct option.
Related Questions
In the given figure, if sides AB, BC, CD and DA of a quadrilateral ABCD touch a circle at points P, Q, R and S respectively, then CR + PB =
BC
AB
CD
AD
In the figure, sides MN, NL and LM of ΔLMN touch a circle at the points A, B and C respectively. If AN = 5 cm, CL = 4 cm and CM = 6 cm, then the perimeter of ΔLMN is :
30 cm
45 cm
60 cm
15 cm
In the figure, AB is a chord of the circle such that ∠AXB = 50°. If AP is tangent to the circle at point A, then ∠BAP = ?
65°
50°
40°
can’t be determined
In the given figure, RT is a tangent touching the circle at S. If ∠PST = 30° and ∠SPQ = 60°, then ∠PSQ is :
40°
30°
60°
90°
