Two circles touch each other externally at P. AB is a direct common tangent to the two circles. If A and B are points of contact and ∠PAB = 65°, then ∠ABP is _________.
25°
In this geometry problem, ∠PAB and ∠ABP are angles on a straight line. So, by linear pair property:
∠PAB + ∠ABP = 90°
Given ∠PAB = 65°
Then, ∠ABP = 90° - 65° = 25°
Similar Questions
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Important Questions from Geometry
A secant PAB is drawn from an external point P to the circle with the centre at O, intersecting it at A and B. If OP = 17 cm, PA = 12 cm and PB = 22.5 cm, then the radius of the circle is:
The central angle of a sector is 80° and whose length is 96π. What is the radius of the circle?
To have a surface area of 9π square units of a ball, what should be the diameter (in units) of the ball?
The area of the sector of a circle (in cm²) of radius 7 cm and central angle 60° is:
(Take π = 22/7)ΔABC is a right-angled triangle with ∠ABC = 90°. If m(AB) = 28 cm, and m(BC) = 96 cm, find the area (in cm²) of the circumcircle of ΔABC. (Use π = 3.14.)
