ABCD is a quadrilateral such that angle D = 90°. A circle touches the sides AB, BC, CD and DA at P, Q, R and S respectively If BC = 24 cm, CD = 25 cm and BP = 6 cm. Find the radius of circle.
1). 7 cm
2). 13 cm
3). 17 cm
4). 6 cm
We use the property that the lengths of pair of tangents from an external point are equal.
Then BP = BQ = 6 cm
QC = BC - BQ = 24 - 6 = 18 cm
CR = QC = 18 cm (tangents from an external point are equal)
RD = CD - CR = 7 cm = SD (tangents from an external point are equal)
Now, angle D = 90°
Let the centre of circle be O.
Then, angle R and angle S in the quadrilateral ORDS is also 90°.
∴, ORDS is a square.
⇒ OR = DS = 7 cm = Radius1. What is the slope of the line 2x - 5y = 12?
2. What are the coordinates of the midpoint of the segment joining points C(5, 2)and D(1, 8).
4. If an exterior angle of a cyclic quadrilateral be $50^{0}$, then the interior opposite angle is :
5. What is the measure of an interior angle of a regular dodecagon?
10. What is the equation of the line which passes through the points (2, 3) and (-4, 1)?