ICSE Class 10CISCE
Share
Notifications

View all notifications

In the Following Figure, a Circle is Inscribed in the Quadrilateral Abcd. If Bc = 38 Cm, Qb = 27 Cm, Dc = 25 Cm and that Ad is Perpendicular to Dc, Find the Radius of the Circle. - ICSE Class 10 - Mathematics

Login
Create free account


      Forgot password?

Question

In the following figure, a circle is inscribed in the quadrilateral ABCD.

If BC = 38 cm, QB = 27 cm, DC = 25 cm and that AD is perpendicular to DC, find the radius of the circle.

 

Solution

From the figure we see that BQ = BR = 27 cm (since length of the tangent segments from an external point are equal)
As BC = 38 cm
⇒ CR = CB − BR = 38 − 27
= 11 cm
Again,
CR = CS = 11cm (length of tangent segments from an external point are equal)
Now, as DC = 25 cm
∴ DS = DC − SC
= 25 − 11
= 14 cm
Now, in quadrilateral DSOP,
`∠`PDS = 90° (given)
`∠` OSD = 90°, `∠`OPD = 90° (since tangent is perpendicular to the
radius through the point of contact)
⇒ DSOP is a parallelogram
 ⇒ OP ∥ SD and  ⇒ PD ∥ OS
Now, as OP = OS (radii of the same circle)
⇒ OPDS is a square. ∴ DS = OP = 14cm
∴ radius of the circle = 14 cm

  Is there an error in this question or solution?

APPEARS IN

Solution In the Following Figure, a Circle is Inscribed in the Quadrilateral Abcd. If Bc = 38 Cm, Qb = 27 Cm, Dc = 25 Cm and that Ad is Perpendicular to Dc, Find the Radius of the Circle. Concept: Chord Properties - the Perpendicular to a Chord from the Center Bisects the Chord (Without Proof).
S
View in app×