Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 10 Answered

there is a cicle with centre o.a triangle ABP is inscribed in it such that the tangent TP at the point P is parallel to AB.prove that APB is an isosceles triangle.
Asked by | 01 Mar, 2013, 04:26: PM
Expert Answer
Join OP and extend it to intersect AB at point Q. Since, PT is the tangent, angle(OPT) = 90. Also, since PT is parallel to AB, so angle(OQB) = angle (OQA) = 90
 
Now, in triangle(AOQ) and triangle (BOQ)
 angle(OQB) = angle (OQA) (90 degree each)
AO = OB  (radius)
OQ = QO (common)
triangle(AOQ) is congruent to triangle (BOQ) (by RHS)
Hence, AQ = QB  (By CPCT)
 
Now in triangle(APQ) and triangle (BPQ)
angle(PQB) = angle (PQA) (90 degree each)
PQ = QP (common)
AQ = QB  (from above)
Hence triangle(APQ) is congruent to triangle (BPQ) (by SAS)
 
So, angle (PAQ) = angle (PBQ) (By CPCT)
Since, sides opposite to equal angles are equal in a triangle
So, AP = PB 
Hence, triangle APB is an isosceles triangle. 
Answered by | 03 Mar, 2013, 06:48: AM
CBSE 10 - Maths
Asked by ajabraosable27 | 11 Oct, 2021, 09:28: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by amikasangma080 | 11 Oct, 2021, 06:14: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by muskanmahek2411 | 08 Oct, 2021, 10:48: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by anishasheoran372 | 13 Jul, 2021, 09:33: AM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by bhilarevishwesh | 21 May, 2021, 08:27: AM
ANSWERED BY EXPERT
CBSE 10 - Maths
Q30
Asked by sangyaswarupa | 16 Mar, 2021, 10:06: AM
ANSWERED BY EXPERT
Get Free Sample Papers
×